Preheat oven to 325 degrees F. Line a flat work surface with a sheet of parchment paper. Place ribs on the parchment in an even layer. Season generously with salt and freshly ground pepper on both sides. Heat a large roasting pan on top of the stove over medium heat. Add the olive oil and let heat for 1 minute. Put the ribs in the pan and brown on all sides, 8–10 minutes. Add the garlic and let brown, 1–2 minutes. Add the crushed tomatoes. Using a wooden spoon, scrape up all the browned bits on the bottom of the pan. Add just enough water to cover the ribs. Transfer to the oven and braise, uncovered, until the meat is tender, 2–2½ hours, checking after 1¼ hours.
Check the ribs after 1¼ hours. The surface of the roasting pan should be caramelized around the edges, with bubbles of sauce around the ribs. Return to the oven until the ribs are fork tender, another 45 minutes.
After a total of about 2 hours of cooking, check for doneness. The meat should be tender and pull easily from the bone. Set ribs aside in the roasting pan to cool slightly.
Bring a large pot of salted water to a boil. Add the rigatoni and cook for 3 minutes less than what's advised on the box. Meanwhile, pull the pork meat from the bones; discard the bones. Toss the meat with the sauce in the roasting pan to make a ragù. Season with salt and pepper. Break up the dried chili and stir into the sauce.
Assembly: Reserve ¾ cup pasta water. Drain the rigatoni, then return to the pot. Pour reserved pasta water and sauce into the pot. Cook over low heat, gently tossing the rigatoni with the sauce for 1–2 minutes to allow it to "marry"—or absorb—the sauce. The pasta should be al dente. Taste for seasoning and adjust if necessary. Transfer to a platter or bowl and serve with freshly grated Pecorino Romano and more dried chilies.