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 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 Dutch oven. 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 to deepen its flavor. Pour in the red wine, scraping up any browned bits from the bottom of the pot. Bring to a boil and allow the wine to 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 come up 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 easily pulls away from the bone.
07 - Carefully remove the 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. If a thicker sauce is desired, reduce the liquid over medium-high heat on the stovetop until it reaches the preferred consistency.
08 - Arrange the short ribs on warmed plates or a platter, spoon the reduced sauce generously over the top, and serve immediately while hot.