01 - Preheat oven to 325°F.
02 - Pat the short ribs dry with paper towels. Season all sides generously with salt and black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Sear the short ribs in batches until deeply browned on all sides, about 2 to 3 minutes per side. Transfer the seared ribs to a plate and set aside.
04 - Add the diced carrots, celery, and onion to the Dutch oven. Cook, stirring occasionally, until the vegetables have softened, about 5 minutes. Stir in the minced garlic and tomato paste, then cook for an additional 1 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. Pour in the beef broth and add the rosemary sprigs, thyme sprigs, and bay leaves. The liquid should nearly cover the meat. Bring to a gentle simmer on the stovetop, then cover with the 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 - Remove the Dutch oven from the oven. Carefully transfer the short ribs and vegetables to a serving platter. Skim any excess fat from the surface of the braising liquid. Discard the rosemary sprigs, thyme sprigs, and bay leaves.
08 - Serve the short ribs hot with the skimmed braising sauce spooned generously over the top. Pair with mashed potatoes, polenta, or crusty bread.