A hearty dish that is wonderful to serve any time of the year. While I like to serve this with the lamb meatballs in addition to the short rib sauce, the dish does not suffer without them.
Preheat oven to 350 degrees. Place oven rack in the lower 1/3 of your oven.
Preheat oil a heavy-bottomed Dutch oven over medium-high heat. Season the short ribs with salt and freshly ground black pepper. Brown the ribs on all sides; you will have to do this in batches, adding more oil as needed. Remove the ribs and set aside.
Add the onion and garlic and cook, stirring frequently, for 3-4 minutes or until slightly softened. Add the tomatoes, wine, and mustard. Bring everything to a boil while scraping the brown bits off the bottom of the pan, preferably with a wooden spoon. Return the short ribs to the pan. Add the beef broth, cover the pan tightly, and cook in the oven for about 2 ½ hours. Check after 1 hour to make sure that you do not need to add any more broth. Then continue to check every half hour until the meat is fork tender and falls easily from the bone.
Meanwhile heat oil in a large sauté pan over medium-high heat. Roll the lamb into 1 tablespoon-sized balls and, working in batches, cook until lightly browned on all sides and cooked through, about 4 minutes. Reserve on a paper towel-lined plate (try to only eat 1 or 2!).
Remove the short ribs from the tomato sauce. Using a large spoon, remove any excess fat from the surface. In small batches, blend the tomato sauce until smooth, adding it to a fresh saucepan (I used my immersion blender and kept everything in the same pot). Remove meat from bones and discard the bones. Using 2 forks, shred the meat and then stir into the sauce. Add lamb meatballs and keep warm over low heat. Season as needed.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until al dente, about 8-10 minutes. Drain the pasta and place in a large serving bowl, reserving some of the pasta water. Using a slotted spoon, remove the meat from the sauce and add to the pasta. Coat the pasta with the sauce, as desired. Toss well. Top each serving with chopped fresh parsley and grated Parmesan before serving.