Offally good: Mark Hix uses cheap cuts to creat delicious, thrifty and old-fashioned favourites

We are obsessed with expensive prime cuts of meat but we don't give a damn about what happens to the rest of the animal. In other European countries, it's normal to shop for cheaper cuts that will stretch the budget and feed the family for less.

I am never quite sure why more people don't like offal but I think the objection is often a psychological one. If I asked you whether you fancied some intestines stuffed with minced meat, fat and herbs you might well turn away in disgust – but then again, if I offered you a plate of Cumberland sausages and mash with onion gravy you'd bite my hand off. I have fond memories of my grandmother's stuffed lamb's hearts when I was younger, but I'm not so sure that many families enjoy treats such as these nowadays...

Calves' sweetbreads with carrots

Serves 4

Calves' sweetbreads aren't a cheap cut, but they are delicious. You will probably need to order calves' sweetbreads in advance from your butcher or try Donald Russell (donaldrussell.com), who sells a great selection of offal and cuts.

800g calves' sweetbreads, soaked in cold water for a couple of hours
700-800g medium carrots, peeled
200ml Riesling
200g butter
1tbsp chopped chervil or parsley
Salt and freshly ground black pepper

Preheat the oven to 200C/gas mark 6. Cut the carrots into 5cm lengths, then square them off, keeping the trimmings for the purée. Cut the lengths into cm batons, adding some to the trimmings so that you have two evenly-sized piles, one of batons and one of batons mixed with trimmings. Put the pile that includes the trimmings into a pan, cover with water and add a teaspoon of salt, bring to the boil and simmer until the carrots are tender; then drain, reserving the cooking liquid, and blend the carrots in a food processor until smooth. Transfer to a saucepan, add a little butter; season to taste. Cut the sweetbreads into 4 evenly sized chunks or, if they are odd shapes, 8 pieces. Heat a tablespoon or so of the vegetable oil in preferably an ovenproof frying pan, season the sweetbreads and fry them on a high heat on all sides until they are nicely coloured and transfer to the oven. After 5-6 minutes, add half of the butter and baste the sweetbreads; return to the oven for another 10 minutes, turning them a couple of times during cooking. Meanwhile, cook the batons of carrots in the liquid from the trimmings for a couple of minutes or until they are cooked but still have a bit of a bite, then drain. Remove the sweetbreads from the pan and keep warm. Drain the fat from the pan, add the Riesling and simmer until there is about a tablespoon left, then remove from the heat and whisk in the remaining butter before adding the batons of carrots and chervil.

To serve, reheat the carrot purée and spoon on to the centre of warmed plates, place the sweetbread on top and spoon the carrots and sauce over.

Sunday brunch salad

Serves 4

This is one of those salads that comes into its own when you have a load of bits and bobs to use up in the fridge.

You don't need to use all of the ingredients I've used here – it all depends on what you have to hand. In fact, we made the most of a freakishly huge (10kg) late-season puffball foraged from Norfolk just before Christmas and diced it up and tossed it into a salad with some chicken livers and bacon and it was absolutely delicious.

A few handfuls of small winter salad leaves and herbs such as rocket, baby spinach, bittercress, pennywort, etc
2-3 thick slices of bread, cut into rough 1cm chunks
150g lambs' liver, trimmed and cut into rough 1cm chunks
150g calves' or lambs' sweetbreads, trimmed and cut into rough 1cm pieces
Vegetable or corn oil for frying
A couple of good knobs of butter
6 thick rashers of streaky bacon
4 duck eggs

For the dressing

1tbsp cider vinegar
2tsp Tewksbury or Dijon mustard
4tbsp rapeseed oil
Salt and freshly ground black pepper

Heat a couple of tablespoons of vegetable oil in a frying pan and cook the cubes of bread for 3-4 minutes on a medium heat, stirring them as they are cooking until nicely browned; then transfer to some kitchen paper on a plate.

Whisk all of the ingredients together for the dressing and season to taste. Season the sweetbreads, heat a little vegetable oil in a heavy frying pan and cook the sweetbreads for 3-4 minutes on a medium heat, turning them as they are cooking then add a knob of butter and cook for a further 2 minutes. Remove the sweetbreads with a slotted spoon and keep warm. Meanwhile, grill or fry the bacon in the same fat until crisp. Season the liver and fry in the same fat with a little more butter just for 2-4 minutes, keeping it pink, then remove and mix with the sweetbreads.

To serve, poach the eggs, arrange the winter salad leaves, offal and bacon on serving plates or in a bowl with the egg in the centre and spoon over the dressing.

Lamb's liver with herbs and green split peas

Serves 4

Lamb's liver is a delicious and cheap lunch and dinner option and what's more it's really quick to cook – a far cry from my childhood memories in which I remember the liver being cooked for hours in the oven until it turned an unsavoury shade of green.

You can slice or dice it or I've even carefully roasted it briefly then carved it like a joint.

8 slices of cleaned lamb's liver about cm thick
3tbsp of chopped green herbs (parsley, chervil, tarragon, fennel)
A couple of good knobs of butter

For the green split pea sauce

60g green split peas, soaked in cold water for an hour
1 medium onion, peeled, halved and finely chopped
4 cloves of garlic, peeled and crushed
2 medium carrots, peeled and cut into small cm dice
2 sticks of celery, peeled if necessary and cut into small cm dice
A couple of good knobs of butter
2tsp flour
tsp tomato purée
500-600ml hot chicken or beef stock

First make the green split-pea sauce: melt the butter in a thick-bottomed saucepan and gently cook the onion and garlic for 2-3 minutes, stirring occasionally until they soften, add the carrots and celery, cover with a lid and continue cooking gently for a few minutes. Stir in the flour and tomato purée then gradually add the stock. Add the green split peas, season and simmer gently for about 30 minutes or until the peas are tender and the sauce is just coating the peas and vegetables.

Season the liver and coat in the herbs. Melt the butter in a frying pan until almost foaming and fry the slices of liver for a minute or so on each side, keeping them nice and pink. Serve the slices of liver on the split pea sauce.

Tripe with black beans and ginger

Serves 4

Years ago, tripe would make a fairly regular appearance on the butcher's counter, especially in the north of England. It's harder to get hold of now, although if you frequent good authentic Chinese restaurants and supermarkets you will certainly come across the stuff. You can serve this as a dim sum dish or as a sharing main course.

Tripe varies; most of the stuff that is on sale these days is the blanched white tripe which is cooked. It doesn't have a great flavour compared to the stuff which is less treated and not so white, which takes longer to cook and which absorbs the flavours much better.

You can buy fermented dried black beans from good Chinese supermarkets; they generally have ginger mixed with them.

500g tripe, washed, dried and cut into rough 2cm chunks
1tbsp sesame oil
1 medium onion, peeled, halved and roughly chopped
6 cloves of garlic, crushed
2 red chillies, sliced
A 40-50g piece of root ginger, scraped and finely chopped
100ml rice wine
500ml chicken stock
3tbsp light soy sauce
60g dry Chinese fermented black beans
2-3tsp cornflour
A few sprigs of coriander to serve

Heat the sesame oil in a heavy saucepan and gently cook the onion, garlic, ginger and chilli for 2-3 minutes until softened. Add the rice wine, chicken stock and soy, bring to the boil, add the tripe and simmer for about 15 minutes. If you are using the un-blanched tripe it may need about an hour to cook as well as more stock.

Dilute the cornflour in a little water and stir in enough to thicken the mixture and continue simmering for another 5 minutes.

Season if necessary and serve with the sprigs of coriander scattered over.