Put a heavy bottom pot on the stove over high heat and add a little olive oil. Add the lamb to sear, and season it with salt and pepper.
Once seared on all sides, move it to a bowl, and add the onions and carrot to the pan. Turn heat to medium and cook the onions and carrot to soften, about 5 minutes. Add in the tomato paste and garlic and cook for 3-5 minutes.
Add the stock to the pan and scrape the bottom to make sure the browned bits stuck to the pan are mixed into the sauce. Stir in the oregano, rosemary, and vinegar, and add the meat back to the pan. Bring to a simmer, turn to low, and cook for about 2 or 3 hours until the meat is falling apart. (this could optimally be done in the oven at 300 if your pan can go in the oven.)
Meanwhile, prepare the pasta according to the package instructions.
Once the meat is ready, stir the meat and pasta together and serve. If the sauce has evaporated too much and seems dry, you can add a little water to loosen it up.