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.