Preheat your oven to 325°F (165°C) or prepare to simmer on the stovetop.
Season short ribs heavily with salt and pepper. In a large Dutch oven, heat oil over medium-high heat. Sear ribs in batches until browned on all sides. Remove and set aside.
Reduce heat to medium. Add onion, carrots, and celery. Cook for 6-8 minutes until softened. Add garlic and tomato paste; cook for another 2 minutes.
Pour in the red wine, scraping the bottom of the pot to release the browned bits. Let the wine reduce by half.
Add the crushed tomatoes, beef broth, thyme, and rosemary. Return the ribs (and any juices) to the pot.
Cover and transfer to the oven for 3 hours, or simmer on the lowest stovetop setting, until the beef is tender and falling off the bone.
Remove ribs from the sauce. Shred the meat with two forks, discarding the bones and any large pieces of fat. Discard herb sprigs.
Stir the shredded meat back into the sauce.
Cook pasta according to package directions until al dente. Toss the pasta directly into the sauce, adding a splash of pasta water if needed to reach your desired consistency.
Garnish with parsley and plenty of Parmesan cheese.