01 - Preheat oven to 325°F.
02 - Pat the short ribs dry with paper towels and season all sides generously with salt and black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Sear short ribs in batches until deeply browned on all sides, about 2–3 minutes per side. Transfer the seared ribs to a plate and set aside.
04 - Add diced carrots, celery, and onion to the Dutch oven. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes. Stir in minced garlic and tomato paste, cooking for 1 additional minute until fragrant.
05 - Pour in the dry red wine, scraping up any browned bits from the bottom of the pot. Bring to a boil and let the liquid reduce by half, about 5 minutes.
06 - Return the seared short ribs to the pot. Add beef broth, rosemary sprigs, thyme sprigs, and bay leaves. The liquid should almost cover the meat. Bring to a gentle simmer on the stovetop, then cover with a tight-fitting lid and transfer to the preheated oven. Braise for 2 hours 45 minutes to 3 hours, or until the meat is fork-tender and falling off the bone.
07 - Carefully remove the ribs and vegetables from the pot. Skim excess fat from the surface of the braising liquid. Discard the spent herb sprigs and bay leaves.
08 - Serve the braised short ribs hot with the reduced sauce spooned generously over the top.