Make the ragu
Heat the oil in a 5- to 6-quart Dutch oven or other heavy-duty pot over medium-high heat until shimmering. Season the lamb on both sides with salt and pepper and sear the meat on one side until well browned, 3 to 4 minutes. Using tongs, turn and sear the other side until browned, 3 to 4 minutes more. Transfer the lamb to a deep platter.
Reduce the heat to medium low and add the carrot, celery, onion, garlic, and herbs. Cook, stirring frequently, until the onion is softened, 7 to 8 minutes. Return the lamb and its juice to the pot, raise the heat to medium high, and pour in the wine. Cook for 1 to 2 minutes and then add the tomatoes. Bring to a boil and then reduce the heat to medium low or low to maintain a gentle simmer. Cover partially and let the sauce simmer until the lamb is forktender, about 2-1/2 hours. Using tongs, transfer the meat to a cutting board and let it cool for a few minutes. Meanwhile, if the sauce seems thin, let it continue simmering until thickened to a saucy consistency. If it seems too thick, add a splash of water.
Shred the lamb with two forks and return it to the pot. Simmer gently until the meat is heated through. Season to taste with salt.
Cook the pasta and serve
When ready to serve, bring a large pot of well salted water to a boil. Cook the pasta until al dente—you want it to still have some bite because it will continue to cook a bit while you’re tossing it with the ragù. Reserve about 1 cup of the cooking water and then drain the pasta. Return it to the pot and toss it with some of the ragù, adding a little cooking water if it seems dry. Serve the pasta with more ragù spooned over the top. Garnish with sahved Parmigiano-Reggiano or Pecorino Romano, if you like, and serve with minced chiles or red pepper flakes on the side.
The ragù can be refrigerated in an airtight container for up to 3 days or frozen for up to 3 months. Reheat gently before tossing with pasta.