Add the olive oil to a large, heavy-bottomed pot over medium-high heat. Pat the surface of the beef short ribs as dry as possible. Season the short ribs with kosher salt and ground black pepper. Once the oil is hot, add in the seasoned short ribs. Cook for 3-4 minutes per side, until nicely browned. Transfer the browned short ribs to a plate and set aside.

Add the soffritto (carrots, onion, and celery) to the same pot, seasoning with kosher salt and ground black pepper. Cook, stirring occasionally, until the soffritto is deeply browned, 15-20 minutes.

Add the garlic to the pot with the soffritto. Cook until fragrant, 1-2 minutes. Add the tomato paste and cook 2-3 minutes, until browned.

Pour the red wine into the pot, stirring constantly to scrape up any browned bits. Cook for 3-4 minutes, until the wine is almost completely absorbed.

Tie the herbs together using kitchen twine, then add to the pot with the bay leaves and parmesan rind (if using). Add the crushed tomatoes, beef broth/stock (or water), and browned short ribs. Stir to combine. Bring to a boil, then reduce heat to low. Cover and simmer for 2 ½ – 3 hours, until the short ribs are fall-apart tender.

Transfer the short ribs to a plate. Remove and discard the spent herbs, bay leaves, and parmesan rind. Shred the short ribs into bite-sized pieces and return to the pot with the ragu.

Bring a large pot of salted water to a boil. Add the pasta and cook until al dente. Reserve about 1 cup of the starchy pasta water, then drain the pasta.

Bring the braised short rib ragu up to a simmer. Stir in the heavy cream and parmesan cheese. Add the cooked pasta to the pot, tossing to coat. Adjust with reserved pasta water if needed. Cook for 1-2 minutes.

Portion the short rib ragu into bowls, topping with additional grated parmesan and fresh herbs as desired. Serve immediately.