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 pot. Sauté until the vegetables are softened, 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. Pour in the dry red wine, using a wooden spoon to scrape up any browned bits from the bottom of the pot. Bring to a boil and let the wine reduce by half, approximately 10 minutes.
05 - Return the seared short ribs to the pot. Pour in the beef broth and add the thyme sprigs, rosemary sprigs, and bay leaves. The liquid should come up to nearly cover the ribs. Bring everything 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 30 minutes to 3 hours, until the meat is fork-tender and falling off the bone.
07 - Carefully remove the short ribs and vegetables to a serving platter. Discard the herb sprigs and bay leaves. Skim any excess fat from the surface of the braising liquid. For a richer, thicker sauce, reduce the liquid on the stovetop over medium heat until it reaches the desired consistency.
08 - Arrange the short ribs on plates and spoon the reduced sauce generously over the top. Serve immediately while hot.