01 - Preheat the oven to 325°F. Pat the beef short ribs thoroughly dry with paper towels and season generously on all sides with kosher salt and freshly ground black pepper.
02 - Heat olive oil in a large Dutch oven or heavy ovenproof pot over medium-high heat. Working in batches if necessary, 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 - Reduce the heat to medium. 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 continue cooking for 1 additional minute until fragrant.
04 - Stir in the tomato paste and cook for 1 minute, coating the vegetables evenly. Pour in the dry red wine, using a wooden spoon to scrape up any browned bits from the bottom of the pot. Bring the liquid to a boil and allow it to reduce by half, approximately 10 minutes.
05 - Return the seared short ribs to the pot along with any accumulated juices. Pour in the beef broth and add the thyme sprigs, rosemary sprigs, and bay leaves. The braising liquid should come up nearly to the top of the ribs. Bring the mixture to a gentle simmer on the stovetop.
06 - Cover the pot with a tight-fitting lid and carefully transfer it to the preheated oven. Braise for 2 hours 30 minutes to 3 hours, or until the meat is fork-tender and pulling away from the bone.
07 - Carefully remove the pot from the oven. Transfer the short ribs and vegetables to a warm serving platter and tent loosely with foil. Discard the thyme sprigs, rosemary sprigs, and bay leaves. Skim any excess fat from the surface of the braising liquid. For a richer, more concentrated sauce, simmer the liquid on the stovetop over medium heat until it reaches the desired consistency.
08 - Arrange the short ribs on warmed plates or a serving platter. Ladle the reduced sauce generously over the ribs and serve immediately.