For the ragu: Preheat the oven to 350 degrees F.
Heat the oil in a large Dutch oven over high heat. Season the beef well with salt; then sear it on all sides, about 8 minutes. Add the tomatoes with their juices, wine, vinegar, fennel seeds, garlic, carrots, celery, bay leaves and onion. Season the liquid with 1 tablespoon salt. Bring to a simmer, cover and transfer to the oven. Cook until the meat is almost tender, about 2 hours. Uncover and cook until the meat is tender all the way through and falling off the bone, 30 to 45 minutes more.
Cool the meat in the braising liquid. Remove and discard the bay leaves. Place the meat on a cutting board and pull it into large bite-size chunks with 2 forks. Remove any fat from the surface of the sauce and discard; return the meat to the sauce. (The dish can be prepared to this point up to 2 days ahead, the cooled, covered and refrigerated.)
For the pasta: Mix the semolina flour and 1 teaspoon salt in a stand mixer fitted with the paddle attachment. Add the eggs, yolks, lemon zest and juice and pepper; mix slowly to make a rough dough. Switch to the dough hook attachment and knead until smooth, about 5 minutes. Form the dough into a ball by hand; cover with plastic wrap and let rest at room temperature for 1 hour.
Divide the dough into 10 pieces and cover with a towel. Roll the dough with a pasta machine into sheets to setting number 6. Dust with semolina and lay on baking sheets; dry for 15 minutes. Then cut into fettuccini with the appropriate attachment. Dust with semolina and set aside on baking sheets; dry for at least 1 hour.
Bring a large pot of water to a boil over high heat and salt it generously. Add the fettuccini and cook, stirring frequently, until al dente, about 4 minutes. Drain and toss with the grated pecorino. Transfer to serving plates. Spoon the meat sauce over the pasta and sprinkle with the parsley.
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