Make sure the brains you buy have been removed from the skull in one piece. Fill a bowl with warm water and wash them gently, removing any small pieces of adhering bone. Take the brains out, fill the bowl with fresh water and leave the brains to sit in it for 30 minutes.
Put the onion, carrot, celery, bay leaves, garlic, cider vinegar, 2 teaspoons salt, 1 teaspoon pepper and 300 ml (11fl oz) cold water into a large, deep pot and boil for 2 minutes, then allow to cool completely. Add the brains to the pot and fill with enough cold water to cover them by 3cm (1 in). Put the pot back on the stove and bring to the boil over a high heat, stirring gently from time to time to stop the brains sticking to the bottom. Once they come to the boil, turn down the heat and simmer for 5 minutes. Then transfer the pot to the sink, turn the cold tap on slowly and run the water gently over the brains until it runs off cold. Take one brain out at a time and separate it into its two lobes, discarding the small round-shaped bit in the middle; also discard the vegetables. Put the divided brains into a bowl and rinse them gently in cold water, then drain.
Heat up a large frying pan and add the butter; keep on a high heat and fry until the butter browns, then add the brains. Fry them for about 4 minutes until golden brown, then turn over and fry for another 4 minutes. To make the sauce, add the balsamic vinegar, stock and ½ teaspoon each of salt and pepper and simmer for 2 minutes. Toast the bread and spread a thick layer of chutney on top. Put three lobes of brain on each piece of toast and spoon the sauce over them.