Tonight, against the dark mountains, the floodlit façade of Our Lady of Guadalupe Monastery looks like heaven's front door. Outside, the restaurants around the fountain are packed – but while we nibble our jamón ibérico tapas, within the vast building 10 monks are at prayer.
Among the tourists are pilgrims, who have come here for 700 years, ever since shepherds unearthed a mother-and-child figurine that was deemed to have been whittled by St Luke. The Guadalupe Virgin's monastery-church became the infant Spanish nation's holiest place.
For the so-called "Catholic Monarchs", Ferdinand and Isabella, who re-Christianised Spain in the 15th century, this part of Extremadura in the west of the country was soon a second home. Here Columbus presented them with the very first capsicum to leave the New World. He called it a pimiento, from the Spanish for pepper. Having fluffed his commission to locate India's real pepper, he hoped this strange, wizened fruit might get him off the hook. One imagines the scene: "But I managed to find this, ma'am." What their majesties made of it, nobody knows, but it proved in the end more useful than gold. In multifarious varieties, from chillies to sweet peppers, it was to fire up and flavour half the world's cuisine.
Prior Guillermo told us of a recently discovered book listing 60 New World plants, including wildly exotic potatoes and tomatoes, delivered by Columbus and the later conquistadors to be cultivated in the monastery garden. Could we see the garden? The prior was surprised. No one had asked before.
From the garden's sunny slopes, the monastery appears monolithic. Paulo, the gardener, says that this is his own piece of paradise. He shows us his plants – tomatoes, haricots, peppers and potatoes, growing where they have flourished for 500 years. Paulo's garden might not be fancy but it is a shrine to vegetarianism, where food plants that are now impossible to imagine life without first put down roots outside the New World. Hands up who'd stay a veggie with just turnips in the pot.
The number of monks has dwindled from 400 in Columbus's day to just 10, but they still grow their food among the olive trees and grapevines. The garden also supplies the monastery hostel. At bargain prices, its 15th-century, five-star ambience includes a private cloister. Our oak-panelled room had no TV, but the four-poster bed might have been slept in by kings.
The monastery in parts rivals the Vatican. Indeed, its sacristy is known as Extremadura's Sistine Chapel. The tiny wooden Señora de Guadalupe remains not only first lady of Spain but of the Spanish-speaking world; with five bejewelled crowns and gold lamé gowns, she is also possibly the richest.
Extremadura is often billed as "undiscovered", yet nowhere in Spain was discovered earlier. Mérida, its capital and now a World Heritage Site, was founded in 25BC by Emperor Augustus as a retirement home for 40,000 legionaries. Designed as a replica of Rome, it became the empire's 10th city. Relics are everywhere: a 15,000-seater amphitheatre, a dazzling marble theatre, a plethora of temples, villa and forums, and a 60-arch bridge across the Guadiana river.
Even many locals believe that "extremadura" means "extremely hard", describing the climate of winter frosts and summer heat. In fact, the Romans named it Extrema Dorii, "the land beyond the Duero river". There are eagle-circled peaks, gorges and waterfalls, green river valleys, olive groves and vineyards. Yet for locals, home is the dehesa, the seemingly endless forests of scrubby oak and cork trees – for centuries, a free-range realm of Iberian black pigs.
If pigs ever picture a perfect piggy paradise, then the dehesa must be it. Porcine monarchs roam for a year grubbing forest herbs, working up big appetites for the autumn bellota glut, when the sweet acorns that give bellota ham its name fall from the oak trees.
Deep in the forest we witness a startling scene. Farmer Navavaca begins a strange, haunting cry. From the trees and hillsides, pigs begin trotting towards him – first a trickle, then a flood, then a stampede. They are big, black and beautiful. A hundred gaze at him expectantly. He has known them since they were piglets; they will become the world's costliest hams.
In the town of Montánchez, hams must be air-cured for a year, then matured for three more. Bellota ham is finite – the forest cannot sustain any more pigs – and prices are soaring. In his cellar, Juan Bautista shows us 3,000 hams. How much for the lot? He winks and shakes his head. They say in Extremadura that every pig is a bank.
Montánchez is typical of the attractive small towns sprinkled like confetti wherever we go. Most have eye-catching castles white houses cascade on to arcaded squares. Yet, even Spanish tourists are rare. Many of these places ooze star potential, but we vote exquisite Llerena the most likely to succeed. Eager to boost tourism, the regional government has converted one mansion into a hospedería – a kind of local parador – the original marble halls of which exude grandee elegance. Chef Francisco recommends the chilled almond soup, duck liver with ham, ham-wrapped monkfish, beef with chorizo (bellota, of course) and olive-oil ice-cream.
Llerena, they whisper, was once the Spanish Inquisition's infamous HQ. It explains why there are so many mansions here: the inquisitors lived well. Heretics were once burned near the town's fountain, but when I helpfully suggest that Inquisition re-enactments would put Llerena on the map, everyone looks horrified: "It's not a thing we're proud of."
Our visit to Zafra, 30 miles to the north-west of Llerena, coincides with its pulsating San Miguel fiesta, where black pigs have been traded since 1381. At the Hotel Huerta Honda we meet champion ham-slicer Manuel Llerena. Knives flashing like wands, he cuts slices so transparent you could read this newspaper through them. Highly trained and highly paid, these champion slicers get poached by other restaurants like celebrity footballers.
To the north, the city of Cáceres was once a conquistador stronghold. And few places can match it in fitting two engaging cities into one. Inside its part-Roman, part-Moorish walls, the old city drowsily dreams of its golden age. It is ringed by marginally younger but wide-awake Cáceres, whose elegant streets, gardens and squares bustle with life.
Time stops at the walls. Every stone of every building – the youngest dates to the 16th century – remains exactly as it was when it was laid. The only sounds are birdsong and the babbling of tour guides: as another World Heritage Site, Cáceres gets coachloads of visitors. Later, in the moonlight, we stroll through the deserted old city. Nothing indicates the century. The films shot here include Ridley Scott's Columbus epic, 1492; the explorer would no doubt still recognise each street.
Due east of Cáceres lies Trujillo, once the conquistador capital, which plunges like a stage set from its crag-perched castle to a grandiose Plaza Mayor. Beside the marble fountain rears a giant bronze statue of its illiterate famous son, Francisco Pizarro, mounted on his steed. The conqueror of Peru and importer of potatoes made his village-sized city the richest in Spain. Granted rights to loot whatever they fancied, several generations of the big Pizarro family brought home the golden bacon. Their huge palaces bluster above narrow lanes. Now a bit crumbly, they still reek of old wealth, ill-gotten or not, like a mummified millionaires' row.
Finally, near Guadalupe, a narrow road lifts us through dense forest to misty heights. There are purple-heather moors; river gorges cleave between serrated peaks. Over 50 serpentine miles we pass a weed-grown Roman temple and a few white mountain villages, and as the radiant mist dissolves we reach the lush La Vera valley, hidden by the Gredos mountains like a verdant Shangri-la.
Everything grows here: asparagus, tobacco, cherries, grapes and pears – even bananas – but pimentos, and pimentón, is what La Vera is about. The monks of nearby Yuste monastery blagged from their Guadalupe brethren the peculiar New World capsicums, then invented the technique that transmutes them into the red gold of pimentón, which spices chorizo and alchemises dishes with smoky hints of autumn.
The fields resemble vineyards. Today they glow with crimson fruit. Each bunch is cut by hand by pickers in sombreros. But for the vibrant colours, it could be a Chinese print. We follow a cart to the nearby smoking shed. Over fragrant oak embers, pimentos dry for 15 days before being ground to scarlet dust. Farmer Angel's family have made pimentón this way for more generations than he can calculate. Grinning, he declares that everything he eats – even boiled eggs – must be coloured red.
At the Hotel Villa Xarahiz it seems that every dish – salads, omelettes, pig cheeks, stewed kid, lamb chops, fried potatoes – incorporates the flavour. (Though no one yet has invented a pimentón dessert. A challenge, Mr Blumenthal?)
By now I may be seeing through rose-tinted glasses, but even the mountains look in the sunset uncannily like pimentó*. In all its many colours, Extremadura has served up a feast, and sipping my La Vera cherry liqueur I dream of second helpings. After all, those travelling conquistadors always came back for more.
Ray Kershaw celebrates the foods of Extremadura on 'The Food Programme' on BBC Radio 4 tomorrow, Sunday 17 February, at 12.30pm, repeated on Monday, 18 February, at 4pm
Going to extremes: Spain's wild west
You probably know Spain well: the great cities of Barcelona, Madrid and Seville, bursting with culture and life; the superb beaches on the Atlantic and Mediterranean shores; the muscular mountains that roll ac ross the nation from the Pyrenees to the Sierra Nevada. Yet few British travellers have ever seen the vast lands of Spain's wild west.
There's no need to venture to Arizona or Utah to see wide-screen drama; just make your way to Madrid and venture west and south-west. As soon as you cross the provincial border from Castilla-La Mancha, the territory takes on an elemental appearance – and you feel you have stepped into a natural drama.
Mighty shoulders of rock, draped with pines, hunch over valleys seemingly without end. The rivers that carve them are punctuated by towns and cities steeped in antiquity and bearing the stamp of Romans and Moors.
Extremeños exported Hispanic culture, too: if you recognise the names of some of the great Latin American cities, that is because the great conquistadores came from Extremadura. Francisco Pizarro, born in Trujillo in 1476, commanded fewer than 200 men yet defeated the Inca empire (and bestowed the city of Trujillo upon the north coast of Peru); his second cousin, Hernán Cortés, left Medellí* to overwhelm the Aztecs in Mexico; the still-sleepy village contrasts with its namesake in Colombia.
Extremadura has so far avoided invasions of tourists and second-home buyers. The climate is partly responsible: deep midwinter and high summer take the temperature to extremes. And partly it is because of the absence of direct flights from Britain. But even when the secret gets out, Spain's wild west will prove tough to tame.
The best approach for travellers with cars is from Plymouth to Santander (Brittany Ferries: 0870 907 6103; www.brittanyferries.co.uk) or Portsmouth to Bilbao (P&O Ferries: 08706 009 009; www.poferries.com). From the north coast, spectacular and mostly excellent roads will take you to the frontier of Extremadura in as little as eight hours. Ryanair (0871 246 0000; www.ryanair.com) flies from Stansted to Salamanca; from there, you can pick up a rental car and reach Extremadura in an hour.
For those using public transport, the best bet is to take the train or fly to Madrid. Buses to Extremaduran destinations leave from Madrid's southern bus station at Mendes Alvaro.
Within Extremadura, the main public transport is buses, though the Madrid-Badajoz railway line cuts through. Links between main towns are good and cheap, but a car is recommended for accessing anywhere off the beaten track (which covers most of Extremadura). Avis (0844 581 0147; www.avis.co.uk) has a good network in the province. A small car, booked in advance, costs around £40 per day, including unlimited mileage.
Hotel Huerta Honda (00 34 924 554 100; www.hotelhuertahonda.com). Doubles from €91 (£70).
Hospedería Mirador de Llerena (00 34 924 870 597; www.hospederiasdeextremadura.es). Doubles from €107 (£88).
Hospedería de Real Monasterio, Guadalupe (00 34 927 36 7000; www.monasterioguadalupe.com). Doubles from €66 (£51).
Hotel Villa Xarahiz, Jaraiz de la Vera (00 34 927 665 150; www.villaxarahiz.com). From €71 (£54).
Parador de Cáceres, Ciudad Monumental, Cáceres (00 34 927 211 759; www.parador.es). Doubles from €142 (£109), room only.
Basilica of Guadalupe, Guadalupe (00 34 927 36 70 00; www.monasterioguadalupe.com). Open daily 9.30am-1pm and 3.30pm-6.30pm; admission €3 (£2.30).
Casa Pizarro Museum, Convento de las Jeronimas 12, Trujillo (00 34 927 322 677). Open daily 10am-2pm, 4-7pm; €1.25 (£1).
Bellota hams, Iberllota, Zafra, Badajoz (00 34 924 55 59 95; www.iberllota.com).
Jamones Casa Bautista, Montánchez (00 34 927 380 311; www.jamonescasabautista.com).
Guided tours of the region are offered by Marco Mangut, a Cáceres guide and historian (00 927 22 23 46; www.guiasdecaceres.com).