01 - Set oven rack to lower-middle position and preheat to 325°F.
02 - Pat the short ribs thoroughly dry with paper towels. Season all surfaces generously with salt and freshly ground black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Working in batches to avoid crowding, sear the short ribs until deeply browned on all sides, approximately 2 to 3 minutes per side. Transfer the seared ribs to a plate and set aside.
04 - Reduce heat to medium. Add the diced carrots, celery, and onion to the Dutch oven. Cook, stirring occasionally, until the vegetables soften and begin to caramelize, about 5 minutes. Stir in the minced garlic and tomato paste, cooking for an additional minute until fragrant.
05 - Pour the dry red wine into the pot, using a wooden spoon to scrape up all the caramelized browned bits from the bottom. Bring the liquid to a boil and allow it to reduce by approximately half, about 5 minutes.
06 - Return the seared short ribs to the Dutch oven, nestling them into the vegetables. Pour in the beef broth and add the rosemary sprigs, thyme sprigs, and bay leaves. The liquid should come nearly to the top of the meat; add additional broth if needed.
07 - Bring the liquid to a gentle simmer on the stovetop. Cover tightly with the lid and transfer to the preheated oven. Braise for 2 hours 30 minutes to 3 hours, until the meat is fork-tender and easily pulls away from the bone.
08 - Carefully remove the Dutch oven from the oven. Transfer the short ribs and vegetables to a serving platter, tent loosely with foil. Skim excess fat from the braising liquid and discard the herb sprigs and bay leaves. Ladle the sauce generously over the ribs and serve immediately.