Preheat your oven to 325°F (163°C).
In a large oven-safe pot or Dutch oven, heat the olive oil over medium-high heat. Season the short ribs with salt and pepper, then sear them in the pot until browned on all sides, about 8-10 minutes. Remove the short ribs and set aside.
In the same pot, add the diced onion, carrots, and celery. Sauté for about 5 minutes, or until the vegetables are softened. Add the minced garlic and cook for an additional minute.
Pour in the red wine, scraping the bottom of the pot to release any browned bits. Let it simmer for 2-3 minutes.
Stir in the crushed tomatoes, beef broth, oregano, thyme, bay leaf, and the seared short ribs. Bring to a simmer.
Cover the pot and transfer it to the preheated oven. Cook for 2.5 to 3 hours, or until the meat is tender and falling off the bone.
Once done, remove the pot from the oven and take out the short ribs. Let them cool slightly, then shred the meat, discarding the bones and excess fat.
Return the shredded meat to the pot and stir to combine. Adjust seasoning with salt and pepper as needed.
Meanwhile, cook the pasta according to package instructions. Drain and toss with a little olive oil to prevent sticking.
Serve the ragu over the pasta, garnished with fresh basil and grated Parmesan cheese.