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 deeply browned, 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 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. Add the beef broth, thyme sprigs, rosemary sprigs, and bay leaves. The liquid should 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, or until the meat is fork-tender and falling off the bone.
07 - Remove the ribs and vegetables to a serving platter. Discard the herb sprigs and bay leaves. Skim excess fat from the braising liquid and reduce on the stovetop until the sauce reaches your desired consistency.
08 - Serve the short ribs hot with the reduced sauce spooned generously over the top. Pair with creamy mashed potatoes, polenta, or crusty bread.