Preheat oven to 300ºF (148ºC). Pat ribs dry, season with salt and pepper. Sear in olive oil until browned on all sides. Transfer to a plate.
Sauté onion, carrot, and celery in same pot until softened. Stir in tomato paste and cook until brick red. Deglaze with red wine, scraping browned bits. Reduce for 3 minutes.
Add beef broth, Parmesan rind, rosemary, and thyme. Return ribs to pot. Cover and braise in oven for 3 hours, checking after 2 hours. Meat should fall apart.
Cook rigatoni 1–2 minutes shy of al dente. Reserve ⅔ cup pasta water before draining.
Remove ribs, discard bones and excess fat. Shred meat and return to sauce.
Add pasta and half pasta water to sauce. Stir to coat. Add more water if needed. Serve with parsley and Parmesan.
