In a large, heavy-bottomed casserole or Dutch oven, heat the olive oil over high heat until smoking. Season the lamb chunks with salt and pepper and add to the pan, working in batches if necessary to avoid overcrowding the pan. Sear the meat on all sides to a dark golden brown. Once the meat is browned, remove to a plate and set aside. Add onions and chili flakes and cook until softened, about 8 minutes, scraping the bottom of the pan to dislodge any browned bits. Add the red wine and basic tomato sauce to the pan and bring to a boil. Return the browned meat into the pan and cook over low heat, covered, for 1 ½ hours or until the meat is very tender.
Remove the meat from the pan and, when it is cool enough to handle, break it apart with a fork. Return it to the pan, add the cardoon, bell peppers, and olives, and simmer for an additional 30 minutes. The mixture should be a thick ragu. Season with salt and pepper to taste. Transfer the ragu to a 12-inch sauté pan and keep hot.
Bring 6 quarts of water to a rolling boil and add 2 tablespoons salt. Cook the pasta in the boiling water according to the package directions until tender but al dente. Drain the pasta, add it to the pan with the ragu, and toss over high heat for 1 minute to coat. Divide evenly among 4 warmed dinner plates, top with grated pecorino, and serve immediately.