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.
Recipe courtesy of Giada De Laurentiis