01 - Preheat oven to 325°F. Position the rack in the lower third of the oven for even heat distribution.
02 - Pat the short ribs thoroughly dry with paper towels. Season all sides generously with salt and freshly ground black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Sear the short ribs in batches, turning every 2 to 3 minutes, until deeply browned on all sides. 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 are softened, about 5 minutes. Stir in the minced garlic and tomato paste, and cook for 1 minute until fragrant.
05 - Pour in the dry red wine, using a wooden spoon to scrape up all the browned bits from the bottom of the pot. Bring to a boil and let the liquid reduce by half, approximately 5 minutes.
06 - Return the seared short ribs to the Dutch oven. Pour in the beef broth and add the rosemary sprigs, thyme sprigs, and bay leaves. The liquid should come up nearly to the top of the meat.
07 - Bring the liquid to a gentle simmer on the stovetop. 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.
08 - Carefully remove the Dutch oven from the oven. Transfer the short ribs and vegetables to a serving platter. Skim excess fat from the surface of the braising liquid. Discard the rosemary sprigs, thyme sprigs, and bay leaves.
09 - Spoon the finished sauce generously over the short ribs. Serve immediately while hot.