Season short ribs generously with kosher salt.
Heat oil in a large Dutch oven over medium high heat. Sear short ribs on all sides in batches to avoid crowding. Transfer to a plate.
If excess fat remains, remove all but 2 tbsp from the pot.
Add onion, celery, carrot, and garlic to the pot. Sauté 3-4 minutes until softened.
Stir in tomato paste, 1 tsp kosher salt, and ½ tsp pepper. Cook 2-3 minutes.
Deglaze with red wine, scraping the bottom of the pot.
Return short ribs to the pot. Add broth and crushed tomatoes.
Tie herbs with kitchen twine into a bundle. Add to pot along with bay leaves.
Bring to a low simmer. Cover, leaving lid slightly ajar. Cook 2½–3 hours, until beef is fork tender.
Remove bay leaves and herb bundle. Shred meat with forks. Discard bones/cartilage if using bone in ribs.
Stir in vinegar. Simmer uncovered 15–30 mins more to thicken if needed.
Cook pasta according to package. Toss with ragu or spoon over top. Garnish with cheese and parsley.