Preheat oven to 325°F (165°C). Season the short ribs generously with salt and black pepper on all sides.

Heat olive oil in a large Dutch oven over medium-high heat. Sear the short ribs in batches until browned on all sides, about 4-5 minutes per side. Remove and set aside.

In the same pot, add chopped onions, carrots, and celery. Sauté until softened, about 5 minutes. Add minced garlic and cook for 1 more minute.

Stir in tomato paste and cook for 2 minutes. Pour in red wine, scraping the bottom of the pot to release any browned bits. Let it simmer for 5 minutes to reduce slightly.

Return the short ribs to the pot. Add beef broth, thyme, and bay leaves. The liquid should almost cover the ribs. Bring to a simmer.

Cover the pot and transfer to the preheated oven. Braise for 2.5-3 hours until the meat is very tender and falls off the bone.

Remove the ribs from the pot. Strain the braising liquid and skim off excess fat. Reduce the sauce on the stovetop if desired. Serve ribs with the sauce.