Season the beef cheeks generously with salt and pepper. Heat one tablespoon of oil in a heavy Dutch oven over medium-high heat and brown the beef on all sides. Transfer it to a plate.
Add the remaining oil, onion, carrots, and celery. Cook until softened and lightly golden, then stir in the garlic and tomato paste for one minute.
Pour in the red wine and scrape up the browned bits. Simmer until reduced by about half, then add the stock, crushed tomatoes, and thyme.
Return the beef to the pot. Cover and simmer very gently for about three hours, turning the cheeks once, until a fork slides through the meat easily.
Remove the beef and thyme. Shred the beef with two forks, return it to the sauce, and simmer uncovered until the ragu is thick enough to coat a spoon.
Cook the pappardelle in salted water until just al dente. Toss it with the ragu, adding a splash of pasta water if needed, and serve with Parmesan.