In a pot, bring about 8 1/2 cups (2 liters) of water to a boil with the cleaned and roughly chopped vegetables and the wine. Cook for 10 minutes. Add the whole or large pieces of stoccafisso, making sure they're fully submerged. Once it returns to a boil, turn off the heat. After 10 minutes, drain the fish and discard the vegetables.

When the fish is cool enough to handle, remove the backbone, skin, and any bones, leaving it in large chunks. Lightly coat the pieces with flour. Meanwhile, heat 2 cups (500 ml) of milk in a pot.

In a large pan, cover the bottom with olive oil and heat it. Add the floured fish and lightly brown it without letting it get golden. Lower the heat and add the anchovies, capers, halved garlic clove, and finely chopped onion or shallots. Pour in the hot milk to cover everything, without sautéing the ingredients first, or it will ruin the dish.

Start cooking over very low heat with the lid slightly ajar so the milk doesn't boil over. Stir gently to prevent sticking.

Stir often with a plastic or wooden spatula, loosening the fish from the bottom without breaking up the pieces. If you prefer a creamy texture, stir more vigorously with a wooden spoon.

If the milk is absorbed too quickly, add more a little at a time. Cook for about 45 minutes, until the fish is tender. By the end, the milk should be absorbed and creamy, and the fish lightly golden.

During cooking, check often and stir to prevent the fish from sticking and burning. The finished dish should be creamy, not dry, and surrounded by a bit of olive oil.