What comes after snow, as the second-most important ingredient of a skiing day? The answer is supper. With the schussing and schlepping in the fresh but oxygen-depleted air of the mountains done, every skier's thoughts turn to the evening meal. And to the fact that on nights such as these it is permissible to eat your fill.

In the days before GoreTex and Polartec, when natural layering was provided by warm cheese and meat fat, French resorts were the best places to eat. Even into the era of nouvelle cuisine, it was Megève that stood out as the ski destination for people who really cared about supper – and maybe lunch, too. But with the retirement (as a result of a skiing accident) of the most eminent local chef, Marc Veyrat, a passing of the baton occurred. It was grasped by Italy's Sudtirol region, up in the Dolomites.

There, among some of the most beautiful mountains on earth, local chefs managed to attract the greatest concentration of Michelin stars anywhere in Italy; and from Lagrein, a subtle grape indigenous to the local valleys, red wines were created which not only beat the best of Bordeaux in blind tastings but also helped to make the Sudtirol pre-eminent among Italy's wine-producing regions.

Now another resort is threatening the status of Alta Badia, the valley which leads the rest of the Sudtirol in the starred chef stakes. It is Lech, in Austria – a country in which Michelin does not even publish a gourmet guide because, so a local ski-marketing man told me, its reputation is for good, sensible food rather than gourmet cuisine.

Lech is generally regarded as something of an old-money resort, conservative in outlook and rather posh. It has long been a haunt of royals from Monaco and Spain; indeed, a habitué of the place told me that Lech was where Juan Carlos of Spain skied by choice, his frequent appearances at Baqueira Beret in the Spanish Pyrenees being no more than an official duty.

The motto of the old Brooklands motor-racing track, "The right crowd, and no crowding", might have been coined for Lech. Since 1990, the resort has hung out a "Full" notice when the slopes threaten to get too crowded; ski-pass sales cease, and the electronic sign on the road up from St Anton advises would-be skiers to turn around.

I have been only an infrequent visitor to Lech, and my taste for the place had nothing to do with food. As someone who likes journeying on skis, I always enjoyed its White Ring circuit, which travels down one side of the valley to nearby Zürs and then back up the other; and the pleasure of buying what are almost bespoke ski-boots from the estimable Strolz family made pilgrimages to its large and excellent skiwear shop essential. (In business since 1921, the family has a remarkable private museum of ski boots.) But last season an Austrian friend advised me of my error in failing to investigate the local cuisine; and I set off in March to have some suppers in what the editor of the Gault Millau restaurant guide to Austria describes as a place of "outstanding gastronomy".

A "Euro-Asian fusion" restaurant might not seem an obvious starting point, but Fux isn't the sort of place to demurely wait its turn. The premises – which include a jazz bar and steakhouse as well as the restaurant – are arresting, though there are hints of monorail station and sports centre in the tubular, extensively glazed structure. In the lobby there's an attention-grabbing "book of the restaurant" on display: a 330-page, hardback volume, it is part manifesto, part recipe book, and mostly a colourful display of photographs of the restaurant's food, kitchen staff and owners, Peter and Martina Strolz (yes, the same family).

But the food, which has won the Fux 15 points (out of 20) in the Gault Millau guide, proved utterly disarming. The spring roll starter, with powerful raw vegetables, mango in the middle and a surrounding foam of wild garlic, was a bold statement of intent, as was an intense lemongrass broth. The main course I chose was a familiar Thai dish, prawns in red curry; it was full of flavour, and the prawns were much better than one might expect in a landlocked country. The Burgenland wines, a 2007 Blaufränkisch and a 2006 Pinot Noir, were both excellent.

My second choice, for lunch rather than supper, was a more classic ski-resort restaurant in Oberlech. Set on the ski slopes just above Lech, this is a small satellite village, unusual in that it has a network of passages beneath the pistes which connect the hotels, chalets and lift stations.

Alongside the main chair-lift base is the Goldener Berg, owned by one of Lech's key hotel families, the Pfefferkorns. A very popular lunch stop, the hotel has two restaurants, the gourmet menu served on a large, sunny terrace.

Here the food is quite traditional, but with a twist. The steamed turbot came not just with gnocchi but also with a warm vinaigrette of diced tomato and olive; the rather good cream soup was based on green curry; the desserts included "Three ways with Tahiti Vanilla". The Gault Millau guide is a fan: the Goldener Berg also gets 15 points.

But in Gault Millau's book it is Thorsten Probost who is Lech's star chef. The Burg Vital hotel where he cooks, also in Oberlech, has 18 points for its restaurant, only one below the top score (20 is the holy grail, and nobody gets that); the guide also chose Probost as its Austrian chef of the year for 2008. He has his own section of the Burg Vital's restaurant, called Griggeler Stuba, in which he produces menus based on local herbs. For me, a non-meat-eater, he cooked a five-course meal of vegetables and salads, with intermediate tastings of plant elements.

Probost's own manifesto makes the Fux "book of the restaurant" feel like a paperback. His volume contains only 282 pages, but the art-quality paper is so thick that the book is hard to lift with a single hand. His food, on the other hand, is incredibly light: each ingredient is presented with a precious fragility which demands careful attention. Typology and treatment have a scientific exactitude. The peppercorns are Indian, the sea salt French; in a trio of liquidised vegetables each one was flavoured with the appropriate herb, sometimes presented as a single leaf. Early in my meal came a trio of salads, each sample-sized: marinated radicchio with chervil on liquidised peas; lambs lettuce on a jus of bell pepper; plain, floppy lettuce on a cauliflower puree.

Every part of the meal was a perfectly rendered little sketch. For true gourmets this would probably be perfection; but it was far too good for me.

I was happy to have my last supper at the Aurelio, a newly opened and exquisitely designed hotel owned by the Russian oligarch Oleg Deripaska. Its kitchen does a classic, straightforward job: excellent ingredients well cooked and simply presented. Crayfish in a champagne nage was a remarkable starter, and the main-course sea bass with Mediterranean vegetables and samphire was just as good. The 2007 Burgenland Pinot Noir was almost the cheapest on the Aurelio's list, but it was the best wine I tasted on the trip.

Curiously, among the four chefs whose food I tasted only one, Probost, has remained at his station for the coming season. But there is every reason to believe that standards will remain high. For judged by the number of Gault Millau-rated restaurants, Lech is by far the best ski resort in Austria for supper.

Getting there

* The closest airports are Innsbruck, served by BA (0844 493 0787; ba.com) from Gatwick from 5 December; or Friedrichshafen in Germany, served from Stansted by Ryanair (0871 246 0000; ryanair.com).

Eating & drinking there

* Fux (00 43 5583 2992; fux-mi.net): four-course menu from €60.

* Goldener Berg Hotel, Oberlech (00 43 5583 22050; goldenerberg.at): four-course menu from €55

* Burg Vital Hotel, Oberlech (00 43 5583 3140; burgvitalhotel.at): five-course menu from €83.60.

* Hotel Aurelio (00 43 5583 2214; aureliolech. com): four-course menu from €69.

Prices do not include wine