Preheat your oven to 325°F (160°C).
Season the short ribs generously with salt and pepper.
Heat olive oil in a Dutch oven over medium-high heat. Sear the short ribs until golden brown on all sides. Remove and set aside.
In the same pot, add chopped onion, garlic, carrots, and celery. Cook until softened, about 5 minutes.
Stir in tomato paste and cook for an additional 2 minutes.
Pour in beef broth and red wine, scraping up any browned bits from the bottom of the pot.
Return the short ribs to the pot, cover, and transfer to the preheated oven.
Braise the short ribs for 3-4 hours, or until the meat is fork-tender and falls off the bone.
Once done, remove the short ribs from the pot and strain the cooking liquid to remove any solids. Skim off excess fat.
Serve the short ribs hot, garnished with fresh herbs, alongside your favorite sides.