In a large, heavy gauged pot, preferably made of terracotta or enameled cast iron, sauté the onion, carrot and celery, very gently, in a generous amount of olive oil until soft and translucent, making sure not let any of them brown. (Add a few drops of water if things start to go that way.) Season generously with salt and pepper as you go.

Add the tripe strips and stir well, so every bit of tripe is well covered with your soffritto. Simmer the tripe for a few minutes to allow it to take on the flavor of the aromatics (insaporire). Then add a splash of white wine, raise the heat, and let the wine cook off.

Now add the canned tomatoes, crushing them with your hands as you add them to the pot, together with the bay leaf, if using. Mix everything well and cover the pot. Turn down the heat to low and let it all simmer for a good 30-45 minutes, until the tripe is quite tender and the sauce well reduced. About halfway through the simmering, add the potatoes, mix them in well, re-cover the pot and continue simmering. When the tripe is tender, if you find the dish too liquid, uncover the pot and raise the heat to reduce for a few minutes, until you have the consistency you like. Taste and adjust for seasoning.

The dish can be eaten just as is, with grated parmesan cheese on top, or served on the side for those who like it. But if you prefer, you can ladle the tripe into an oven-proof serving dish (or individual bowls) and top it with a generous grating of parmesan cheese and dots of butter here and there. Place in a moderate oven (180C/350F) for about 10-15 minutes, or until the tripe is bubbling away and the cheese has melted and browned nicely. Let the tripe cool for a few minutes before serving.