Mince the pancetta, salami and prosciutto together to form a paste. In a large, heavy-bottomed pot, heat the olive oil and add the pork paste. Cook over medium heat to soften but not color. Add the beef and brown well on all sides so that a deep brown crust is formed. Remove the beef and set aside.
To the same pan, add the onions, carrots, and celery and cook 1 to 2 minutes, to soften but not brown. Add the tomatoes, 1/2 teaspoon salt, and wine and bring to a simmer, scraping the bottom of the pot with a wooden spoon to loosen browned bits. Return the beef to the pot, cover the pot tightly and cook over low heat for 2 1/2 hours or until the meat is fork-tender. Remove the meat from the pan and allow to rest 15 minutes before serving.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Cook the mezzani according to package directions, until tender yet al dente. Drain the pasta and add it to the pan with the meat sauce. Toss over high heat 1 minute to coat the pasta. Serve the pasta first, then the meat.