Preheat your oven to 325°F (160°C).

Season the beef short ribs generously with salt and pepper. In a large Dutch oven, heat the olive oil over medium-high heat. Sear the short ribs on all sides until browned, about 3-4 minutes per side. Remove the ribs and set aside.

In the same pot, add the chopped onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables are softened. Add the minced garlic and cook for an additional minute.

Stir in the red wine, scraping the bottom of the pot to release any browned bits. Bring to a simmer and let it cook for about 5 minutes.

Add the beef broth, tomato paste, thyme, bay leaves, and the seared short ribs back into the pot. Ensure the ribs are mostly submerged in the liquid.

Cover the pot with a lid and transfer it to the preheated oven. Braise 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 let it sit for 10 minutes. Discard the bay leaves and skim off any excess fat from the surface.

Serve the short ribs with the braising liquid spooned over the top, garnished with chopped parsley.