01 - Preheat the oven to 325°F.
02 - Pat the beef ribs dry and season evenly with salt and black pepper.
03 - Heat olive oil in a large oven-safe Dutch oven over medium-high heat. Sear the ribs in batches until browned on all sides, approximately 2 to 3 minutes per side. Remove and set aside.
04 - In the same pot, add chopped onion, carrots, and celery. Sauté for 5 minutes until softened. Add minced garlic and cook for an additional minute.
05 - Stir in tomato paste and cook for 1 minute. Pour in red wine, scraping the bottom of the pot to loosen browned bits. Simmer for 3 to 4 minutes to reduce slightly.
06 - Add beef broth, thyme sprigs, rosemary sprigs, and bay leaves to the pot. Return the ribs to the pot, ensuring they are mostly submerged.
07 - Bring to a simmer, cover, and transfer the pot to the oven. Braise for 2 to 2.5 hours, or until ribs are tender and nearly falling off the bone.
08 - Remove ribs and vegetables to a serving platter. Discard herb sprigs and bay leaves. Skim excess fat from the sauce and simmer uncovered on the stove for 10 minutes to thicken if desired. Spoon sauce over ribs before serving.