Rinse the tripe under running water, drain it and cut it into thin slices.
Thinly chop the carrot, the celery, the onion and the parsley and sauté in a large pot with a generous drizzle of extra virgin olive oil. When it gets golden and soft, add the tripe slices and stir to enhance the flavour for a few minutes.
In the meantime, peel the ripe tomatoes, chop and purée them to have a smooth tomato sauce, water down with a cup of water and pour it into the pan over the tripe. Season with salt and pepper and simmer covered for about 40 minutes, paying attention not to let it dry out.
The liquid amount will depend on the kind of tomato you chose. So, at the end of cooking, if the tripe is not yet cooked through, add some more water. If it is too watery instead, let it cook without lid for a few more minutes.
At last, the tripe should have a nice thick tomato sauce to eat with tons of Tuscan bread. Before eating, sprinkle with a large spoonful of grated Parmigiano.