Put the flour in a bowl and make a well in the centre. Whisk in the eggs and mustard and continue to whisk until just smooth. Gradually add the milk and a pinch of salt and whisk to a smooth batter. Place in the fridge for at least four hours, but preferably overnight.
Preheat the oven to 220C/200C Fan/Gas 7.
Pour three-quarters of the beef dripping in a roasting tin and heat in the oven. Heat a frying pan and add the remaining dripping. When it’s melted, add the sausages and fry on each side until browned.
Remove the batter from the fridge and whisk once more to combine.
Put the sausages in the roasting tin and pour over the batter. Place in the oven for 30 minutes. Briefly open the oven door to allow the steam to escape and cook for a further 10 minutes.
Meanwhile for the vegetables, put the butter, salt, sugar and 200ml/7fl oz of water in a deep sauté pan. When the butter has melted add the carrots and cook for 3-4 minutes.
Bring a large pot of salted water to the boil, add the peas and cook for 2-3 minutes. Drain the peas and add a little butter.
Heat the veal jus and season with salt and pepper.
Cut a section of the toad in the hole and place on a plate, pour over the jus and serve the vegetables alongside.