Pat the bone-in beef short ribs dry with paper towels, then season generously with salt and pepper. In a large Dutch oven or heavy pot, heat olive oil over medium-high heat until shimmering. Sear the ribs on all sides until beautifully browned, about 3-4 minutes per side. Remove the ribs and set aside.

In the same pot, reduce heat to medium and add diced yellow onion, carrots, and celery. Sauté for about 5-7 minutes until they soften and begin to caramelize. Add minced garlic and cook for an additional minute. Stir in tomato paste and let it cook for another 2 minutes.

Pour in dry red wine, using a wooden spoon to scrape the bottom of the pot. Increase heat and let the wine simmer for about 2-3 minutes. Stir in crushed tomatoes, tomato sauce, and beef broth. Bring to a gentle simmer.

Return the seared short ribs to the pot, add bay leaves, dried thyme, and dried rosemary. Cover the pot with a lid, reduce heat to low, and let simmer gently for 3 to 4 hours.

Remove the short ribs from the pot and place on a cutting board. Allow to cool for a few minutes, then shred the meat off the bones. Return shredded meat back to the pot and let it simmer uncovered for an additional 20-30 minutes to thicken.

Bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente, about 8-10 minutes. Reserve a cup of pasta water before draining. Drain and set aside briefly, tossing with a little olive oil.

Toss the cooked pasta into the pot with the short rib ragu, mixing thoroughly to ensure every strand is coated in the sauce. If needed, add a splash of reserved pasta water for consistency. Serve hot, garnished with fresh parsley and Parmesan cheese.