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In a large Dutch oven, heat 3 tablespoons of the olive oil and, when hot, add the oxtails and cook, turning occasionally, until well browned on all sides, about 10 minutes. Add the pancetta, chopped onion, carrot, and celery and saute until the vegetables are very tender, about 6 minutes. Add the garlic, bay leaves and parsley and cook until fragrant, 1 to 2 minutes. Add the tomato paste and cook, stirring, until lightly browned, 2 to 3 minutes. Add 1 cup of the wine and cook, stirring and scraping the bottom of the pan to release any browned bits, until nearly evaporated. Add the remaining wine and broth and bring to a boil. Return the oxtails to the pan and return to a boil. Cover the Dutch oven and reduce the heat to a simmer. Cook, stirring occasionally, for 2 1/2 to 3 hours, or until the meat is very tender and easily pulls away from the bone. Using tongs or a slotted spoon, transfer the oxtail pieces to a large plate and set aside to cool. Using a spoon, skim any fat that has accumulated on the top of the sauce and discard. Continue to cook the sauce until it has reduced to a sauce consistency and coats the back of a spoon. Keep warm. When the oxtail pieces have cooled enough to handle, remove the meat from the bones, shred into bite size pieces, and return the meat to the sauce. Cover and keep warm.
While the sauce is cooking, roll the pasta dough into sheets about 1/16-inch thick. Using a sharp knife, cut the rolled out pasta into 3-inch squares using a scalloped pastry wheel and set aside on a plate or baking sheet in the refrigerator, covered, until sauce is finished and you are ready to cook the pasta.
Bring a large pot of cold water to a boil and add salt to taste. Add the pasta squares and cook for 1 to 2 minutes, depending on the thickness of the pasta. The pasta should be al dente. Transfer the pasta to a large bowl and toss with the remaining tablespoon of extra- virgin olive oil. Divide the pasta evenly among 6 plates, and ladle the sauce over each serving of pasta. Garnish with freshly grated Parmigiano-Reggiano, sprinkle with parsley and mint and serve immediately.
Take a handful of dough at a time and form into a firm ball. Repeat with the remaining dough. Roll out each dough ball into desired shape in a pasta machine according to the manufacturer's instructions.
Yield: about 1 3/4 pounds fresh pasta