Season the beef generously with salt and pepper. Heat the oil in a large Dutch oven over medium-high heat. Working in batches, sear the beef until deeply browned, 3 to 4 minutes per side. Transfer to a plate.

Add the onion, carrots and celery and cook until softened and lightly browned, 6 to 8 minutes. Add the tomato paste and cook for 1 minute. Add the garlic and cook for 30 seconds.

Add the wine, scraping up any browned bits. Simmer until reduced by half, 8 to 10 minutes.

Add the beef broth, rosemary, thyme and bay leaves. Return the beef and its juices to the pot. Place a piece of parchment directly over the surface, cover and transfer to the oven. Braise until the beef is very tender, 3½ to 4 hours.

About 20 minutes before the beef is done, cook the rigatoni in generously salted water until just shy of al dente. Reserve ½ cup/120 milliliters pasta water, then drain.

Transfer the beef to a plate and shred. Discard the herbs and bay leaves. Purée the braising liquid with an immersion blender, then strain through a fine-mesh sieve.

Return the sauce to the pot. Add the pasta and shredded beef, tossing with the reserved pasta water until glossy and well coated.

Remove from the heat and stir in the Parmesan and parsley. Season with salt and pepper and serve with additional Parmesan.