01 - Preheat 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 over medium-high heat until shimmering. 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 browned ribs to a plate and set aside.
03 - Reduce heat to medium. Add the diced onion, carrots, and celery to the Dutch oven and sauté until 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 to caramelize. Pour in the red wine, using a wooden spoon to scrape up any fond from the bottom of the pot. Bring to a boil and let the liquid reduce by approximately half, about 10 minutes.
05 - Return the seared short ribs to the Dutch oven along with any accumulated juices. Add the beef broth, thyme sprigs, rosemary sprigs, and bay leaves. The braising liquid should come nearly to the top of the ribs. Bring the mixture to a gentle simmer on the stovetop.
06 - Cover the Dutch oven 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 pulls easily away from the bone.
07 - Carefully remove the ribs and transfer to a warmed serving platter. Discard the thyme sprigs, rosemary sprigs, and bay leaves. Skim excess fat from the surface of the braising liquid. For a richer, more concentrated sauce, simmer the liquid on the stovetop until it reaches the desired consistency.
08 - Arrange the short ribs on warmed plates and ladle the reduced sauce generously over the top. Serve immediately.