Sear the Short Ribs: Pat the short ribs dry with paper towels and season generously with salt and pepper. Heat olive oil in a large Dutch oven over medium-high heat. Sear the short ribs on all sides until deeply browned, about 3-4 minutes per side. Work in batches to avoid overcrowding the pot. Remove the short ribs from the Dutch oven and set aside.

Sauté the Vegetables: Add the chopped onion, carrots, and celery to the Dutch oven and cook over medium heat until softened, about 8-10 minutes. Add the minced garlic and cook for another minute until fragrant.

Build the Flavor: Stir in the tomato paste and cook for 2 minutes, allowing it to caramelize slightly. Deglaze the pot with red wine, scraping up any browned bits from the bottom. Let the wine reduce by half, about 3-5 minutes.

Combine and Braise: Add the crushed tomatoes, diced tomatoes, beef broth, bay leaves, oregano, and red pepper flakes (if using) to the Dutch oven. Season with salt and pepper. Return the short ribs to the pot, ensuring they are mostly submerged in the liquid.

Slow Cook: Bring the mixture to a simmer, then cover the Dutch oven and transfer it to a preheated oven at 325°F (160°C). Braise for 3-3.5 hours, or until the short ribs are fall-apart tender.

Shred the Meat: Remove the Dutch oven from the oven and let it cool slightly. Remove the short ribs from the pot and shred the meat using two forks. Discard the bones and any large pieces of fat.

Finish the Ragu: Return the shredded meat to the Dutch oven and stir it into the sauce. Simmer the ragu over low heat for another 15-20 minutes, allowing the flavors to meld. Taste and adjust seasoning as needed.

Cook the Pasta: While the ragu is simmering, cook the pasta according to package directions. Drain the pasta, reserving about 1 cup of pasta water.

Combine and Serve: Add the cooked pasta to the Dutch oven with the ragu. Toss to coat, adding a little pasta water if needed to create a creamy sauce. Serve immediately, garnished with fresh parsley and grated Parmesan cheese.