Pat the beef dry and season with salt and pepper. Heat 2 tablespoons olive oil in a Dutch oven over medium-high heat and sear the beef in batches, about 3 minutes per side, until deeply browned. Remove and set aside.
Add the remaining tablespoon of oil, sliced onions, carrots, and celery to the pot. Cook over low heat, stirring every 10 minutes, for about 75 minutes, until the onions are deep amber and mostly collapsed.
Stir in the tomato paste and garlic and cook for 2 minutes, until the paste darkens slightly.
Pour in the white wine, scraping up any browned bits, and simmer 2–3 minutes until slightly reduced.
Return the beef to the pot along with the beef broth, parmesan rind, and bay leaves. Bring to a gentle simmer.
Cover and braise in a 325°F (163°C) oven, or over the lowest stovetop heat, for 3 to 3½ hours, until the beef shreds easily with a fork.
Remove the parmesan rind and bay leaves. Shred the beef directly in the pot with two forks, stirring it back into the sauce. Taste and adjust salt.
Cook the pasta according to package directions, reserving ½ cup of pasta water. Toss the pasta with the sauce, adding a splash of pasta water if needed to loosen it.
Serve topped with grated pecorino romano and fresh parsley.