Preheat oven to 325°F (165°C). Season short ribs generously with salt and pepper.
Heat olive oil in a Dutch oven over medium-high heat. Sear ribs in batches, about 3–4 minutes per side, until deeply browned. Remove and set aside.
Add onion and carrots to the pot, cooking 6–7 minutes until softened. Add garlic and cook 1 minute more.
Pour in red wine, scraping up browned bits, and simmer 3–4 minutes to reduce slightly.
Stir in broth and tomato paste.
Return short ribs to the pot, add thyme, cover, and transfer to the oven.
Braise 2 to 2 1/2 hours, until the meat is falling off the bone.
Skim excess fat from the sauce before serving.