Step 1Rinse the tripe well and cut it in thin shreds, about 1/4-inch thick. It's easiest to do this with the smooth side up.
Step 2Heat the olive oil in a large skillet over medium heat along with the prosciutto fat and the garlic. Tightly tie the sage, rosemary and cloves in a cheesecloth bundle and add it to the pan. Add the carrot, celery and onions. Cook until the vegetables are soft and just beginning to brown, about 10 minutes.
Step 3Add the shredded tripe, the wine corks and the red pepper flakes and continue cooking. After about 10 minutes the tripe will be swimming in moisture. Add the chunk of cheese and the shallot and cook until that moisture has reduced to an almost sauce-like consistency, about 20 minutes.
Step 4Add the tomato puree and cook another 10 minutes. Add the sparkling water and reduce the heat to low. Cover and cook until the tripe is quite tender and the moisture has reduced to a sauce-like consistency, thick enough that the shreds of tripe cling to each other, about 3 hours. If the tripe starts to dry out, add more tomato puree and sparkling water, up to 1 cup of each.
Step 5Remove the piece of prosciutto fat, wine corks, cheese chunk and garlic, sprinkle with parsley and serve.