01 - Preheat oven to 325°F. Pat the beef short ribs thoroughly dry with paper towels and season generously on all sides with salt and freshly ground black pepper.
02 - Heat olive oil in a large Dutch oven or heavy ovenproof pot over medium-high heat. Sear the short ribs on all sides until a deep golden-brown crust forms, approximately 3 to 4 minutes per side. Transfer the seared ribs to a plate and set aside.
03 - Add the chopped onion, carrots, and celery to the same pot. Sauté until the vegetables are softened and lightly caramelized, about 5 minutes. Add the minced garlic and cook for 1 additional minute until fragrant.
04 - Stir in the tomato paste and cook for 1 minute to deepen its flavor. 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, approximately 10 minutes.
05 - Return the seared short ribs to the pot along with any accumulated juices. Add the beef broth, thyme sprigs, rosemary sprigs, and bay leaves. The liquid should come up nearly to the top of the ribs. Bring to a gentle simmer on the stovetop.
06 - Cover the pot with a tight-fitting lid and transfer to the preheated oven. Braise for 2 hours 45 minutes to 3 hours, or until the meat is fork-tender and falling off the bone.
07 - Carefully remove the ribs and vegetables to a serving platter. Discard the spent herb sprigs and bay leaves. Skim any excess fat from the surface of the braising liquid. For a richer, more concentrated sauce, reduce the liquid on the stovetop over medium-high heat until it reaches the desired consistency.
08 - Serve the braised short ribs hot with the reduced sauce spooned generously over the top. Pair with creamy mashed potatoes, polenta, or crusty bread to soak up the flavorful braising liquid.