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 without crowding the pot, browning on all sides for 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 are softened, about 5 minutes. Stir in the minced garlic and tomato paste, cooking for an additional 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 the liquid to a boil and let it reduce by half, approximately 5 minutes, to concentrate the flavors.
06 - Return the seared short ribs to the pot along with any accumulated juices. Add the beef broth, rosemary sprigs, thyme sprigs, and bay leaves. The liquid should come up nearly to the top of the meat. Bring to a gentle simmer on the stovetop, then cover with a tight-fitting lid.
07 - Transfer the covered Dutch oven to the preheated oven. Braise for 2 hours and 45 minutes to 3 hours, or until the meat is fork-tender and easily pulls away from the bone.
08 - Remove the Dutch oven from the oven. Carefully transfer the short ribs and vegetables to a serving platter. Skim excess fat from the braising liquid and discard the herb sprigs and bay leaves. Ladle the sauce generously over the ribs and serve hot.