Boil the tripe for 15 minutes in salted water with a whole onion, carrot and celery to remove the last of the odor. Drain and set aside.
Sauté the Tripe
Coat the bottom of a skillet generously with olive oil. Sauté the chopped onion, carrot and celery over medium-low heat until the onions start to appear translucent.
Add the tripe to the vegetables and salt and pepper to taste. Cook for a few minutes over medium heat.
Add a ½ cup of white wine. Stir, and cook until the wine has evaporated.
Make the Sauce
Add crushed tomato and a 1 1/2 cups of water to the tripe.
Bring the sauce to a boil. Add a handful of fresh mint and a pinch of salt.
Cover and cook the tripe in the sauce over medium-low heat for 2 hours.
Finish with Pecorino Cheese
After the two hours, turn off the heat and add about 4 Tbs of freshly grated Pecorino Romano cheese. Stir to melt the cheese. Feel free to top with more pecorino when you serve the dish.
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Notes
Pre-Cook the TripeEven if the tripe you've purchased is already clean, boil it in salt water with onion, carrot and celery for 15 minutes to remove any lingering odor.