1. Heat 2 tablespoons of olive oil in a heavy-bottomed pot over medium-high heat. Dry the short ribs with paper towels, season with salt and pepper, and sear them for 3-4 minutes on each side until deeply golden brown. Transfer to a plate and leave 2 tablespoons of drippings in the pot.
2. Add the carrots, onion, and celery to the pot, season with salt and pepper, and cook over medium heat until deeply browned, about 15-20 minutes.
3. Add the garlic and cook for 1-2 minutes until fragrant. Stir in the tomato paste and cook for 2-3 minutes until browned.
4. Deglaze the pot with red wine, scraping the browned bits off the bottom. Cook until the wine is mostly absorbed.
5. Tie the herbs with kitchen twine for easy removal, and add them along with the bay leaves and parmesan rind (if using) to the pot. Add crushed tomatoes, broth, and short ribs. Bring to a boil, then reduce to a simmer and cover. Cook for 2½ to 3 hours until the meat is tender, adding water if necessary to prevent drying.
6. Remove the ribs and shred the meat, discarding the bones. Remove and discard the herbs, bay leaves, and parmesan rind. Return the shredded meat to the sauce.
7. Cook pasta in salted boiling water until al dente, reserving 1 cup of pasta water before draining.
8. Heat the ragu sauce to a simmer. Stir in heavy cream and ½ cup parmesan cheese. Add the cooked pasta and toss to coat well. Adjust the sauce thickness with reserved pasta water if needed. Serve topped with extra parmesan and fresh herbs if desired.