Preheat and Prep: Preheat your oven to 325°F (163°C). Pat the short ribs dry with paper towels and season them generously with salt and pepper. Lightly coat the short ribs with flour.
Sear the Ribs: Heat the olive oil in a large Dutch oven over medium-high heat. Add the short ribs in batches, searing them on all sides until they are browned and crusty, about 3-4 minutes per side. Remove the ribs and set them aside.
Cook the Vegetables: In the same pot, add diced onion and cook until translucent and softened. Then, add diced celery stalks and diced carrots, cooking until the vegetables are tender (about 5-7 minutes). Add the garlic and cook for an additional minute until fragrant.
Add Tomato Paste: Stir in the tomato paste, cooking for about 2 minutes until it darkens and coats the vegetables.
Deglaze with Wine: Pour in the red wine, scraping up any browned bits from the bottom of the pot. Bring the mixture to a simmer and cook until the wine is reduced by half, about 10 minutes.
Add Broth and Herbs: Return the short ribs to the pot. Add the beef broth, thyme sprigs, and bay leaves. The liquid should almost cover the ribs.
Braise: Bring the liquid to a simmer, then cover the pot with a lid and transfer it to the preheated oven. Braise the short ribs for 2.5 to 3 hours, or until the meat is fork-tender and falling off the bone.
Finish and Serve: Remove the short ribs from the pot and strain the sauce to remove the vegetables and herbs. Skim off any excess fat from the surface of the sauce. Serve the short ribs with the reduced sauce poured over the top.