01 - Preheat oven to 325°F.
02 - Pat the short ribs dry with paper towels and season all sides generously with salt and pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Sear short ribs in batches until deeply browned on all sides, about 2 to 3 minutes per side. Transfer to a plate and set aside.
04 - Add carrots, celery, and onion to the pot. Cook, stirring occasionally, until softened, about 5 minutes. Add garlic and tomato paste, stirring for 1 minute until fragrant.
05 - Pour in red wine, scraping up any browned bits from the bottom of the pot. Bring to a boil and reduce liquid by half, about 5 minutes.
06 - Return seared short ribs to the pot. Add beef broth, rosemary sprigs, thyme sprigs, and bay leaves. The liquid should almost cover the meat.
07 - Bring to a gentle simmer on the stovetop, then cover with the lid and transfer to the preheated oven. Braise for 2 hours 45 minutes to 3 hours, until meat is fork-tender and falling off the bone.
08 - Remove ribs and vegetables from the pot. Skim excess fat from the sauce surface. Discard herb sprigs and bay leaves. Serve ribs hot with sauce spooned generously over the top.