Preheat oven to 300°F and adjust racks for a large Dutch oven.
Season short ribs with salt and pepper, then sear in hot olive oil until browned on all sides.
Remove ribs and sauté carrots and onions in the remaining fat until soft. Add garlic and cook for 2 minutes.
Stir in tomato paste, cook for 3 minutes, then add red wine and scrape up brown bits.
Add plum tomatoes, thyme, and bay leaf. Return short ribs, cover, and bake for 3 hours (2 hours covered, 1 hour partially uncovered).
Shred the meat, discard bones and fat, and return meat to the pot. Adjust seasoning.
Cook pappardelle until al dente, then toss with ragu and reserved pasta water if needed. Serve with grated Parmigiano Reggiano.