01 - Preheat oven to 325°F.
02 - Pat the short ribs dry with paper towels and season all sides generously with salt and 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 to 3 minutes per side. Transfer the browned ribs to a plate and set aside.
04 - Add the diced carrots, celery, and onion to the pot. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes. Stir in the minced garlic and tomato paste, and cook for 1 minute until fragrant.
05 - Pour in the 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 the beef broth, rosemary sprigs, thyme sprigs, and bay leaves. The liquid should come up to 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 30 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 any 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 sauce spooned generously over the top.