To make the batter, sift the flour into a large bowl. Add the salt and pepper.
Make a well in the centre of the flour and crack in the eggs. Using a wooden spoon, gradually beat the eggs into the flour then slowly beat in the milk until the batter is the consistency of double cream.
Strain and push any remaining lumps through a sieve. Stir in the thyme. Cover and leave to stand for 30 minutes, or ideally 3-4 hours.
Preheat the oven to 200C/400F/Gas 6.
Heat a large non-stick pan and cook the sausages over a medium heat until golden-brown all over. (If you do not have a non-stick pan add a little oil.) Turn off the heat and brush the sausages with the mustard. Set aside.
Place the dripping or white vegetable fat into an ovenproof dish and heat in the oven for five minutes or until the dripping is hot and hazy.
Add the sausages to the hot dish and pour in the batter. Immediately return the dish to the oven and cook for 35-40 minutes until well-risen and golden-brown.
Serve seasoned with black pepper and a large knob of butter.
If you're making this recipe for vegetarians, make sure you use vegetable fat or butter and vegetarian sausages.