Place an oven rack in the lower 1/3 of the oven. Preheat the oven to 350 degrees F.
Season the ribs with salt and pepper. In a large heavy-bottomed Dutch oven or ovenproof stock pot, heat the oil over medium-high heat. In batches, add the ribs and brown on all sides, about 8 to 10 minutes. Remove the ribs and set aside. Add the onion and garlic and cook, stirring frequently, for 2 minutes. Add the tomatoes, wine and mustard. Bring the mixture to a boil and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Return the ribs to the pan. Add the beef broth, cover the pan and place in the oven for 2 1/2 hours until the meat is fork-tender and falls easily from the bone.
Remove the ribs from the cooking liquid. Using a large spoon, remove any excess fat from the surface of the cooking liquid. Using a ladle, transfer the cooking liquid in the bowl of a food processor. Process until the mixture is smooth. Pour the sauce into a saucepan and keep warm over low heat. Remove the meat from the bones. Discard the bones. Using 2 forks, shred the meat into small pieces. Stir the shredded meat into the sauce. Season with salt and pepper, to taste.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. Drain the pasta and place in a large serving bowl. Using a slotted spoon, remove the meat from the sauce and add to the pasta. Pour 1 cup of the sauce over the pasta. Toss well and thin out the pasta with more sauce, if needed. Sprinkle the pasta with Parmesan cheese and chopped parsley before serving.