Pulse the onion, carrot, and celery in a food processor until finely minced.
Pat the pork shoulder and belly dry. Working in batches, sear the meat in the Dutch oven over high heat until a deep mahogany crust develops on all sides.
Reduce the heat to medium. Add the Italian sausage and prosciutto ends, breaking the sausage apart with a wooden spoon. Once the fats have rendered, add the minced vegetables and garlic, sautéing until the onions are translucent and have picked up the browned bits from the meat.
Stir in the tomato paste and cook for 2 minutes to toast the sugars. Pour in the red wine to deglaze the pot.
Add the crushed tomatoes, bone broth, and aromatics. Return the meat and juices to the pot and bring to a bare simmer. Cover with a tight-fitting lid and transfer to a 300°F (150°C) oven for 3 to 3.5 hours.
Remove the pot and discard the bay leaves. Use a wooden spoon to stir the sauce; the pork shoulder should effortlessly fracture into silken ribbons while the pork belly provides a buttery texture.
Boil your pappardelle until just shy of al dente. Add the pasta directly into the Dutch oven with a splash of starchy pasta water.
Once the pasta and sauce are tossed, remove the pot from the heat and let it sit for 2–3 minutes before plating.
Plate the ragù and finish with high-quality Parmigiano-Reggiano and a final crack of black pepper.