01 - Set the oven to 320°F (160°C) to prepare for braising.
02 - Pat the beef shanks dry and season thoroughly with salt and freshly ground black pepper.
03 - Heat olive oil over medium-high in a Dutch oven or ovenproof pot. Sear beef shanks on all sides until deeply browned, approximately 3 to 4 minutes per side. Remove and set aside.
04 - In the same pot, add chopped onion, sliced carrots, and celery. Cook for 5 minutes until softened. Add minced garlic and sauté an additional 1 minute.
05 - Stir in tomato paste and cook for 1 minute to develop flavor.
06 - Pour in dry red wine, scraping the browned bits from the bottom. Let it simmer for 2 minutes to reduce slightly.
07 - Return beef shanks to the pot. Add beef stock, fresh rosemary, thyme sprigs, and bay leaves.
08 - Bring to a simmer on the stovetop, then cover and transfer to the oven. Cook for 3 hours, turning shanks halfway through, until meat is fork-tender and falling off the bone.
09 - Remove herb sprigs and bay leaves. Skim excess fat if preferred and adjust seasoning. Serve beef shanks with braised vegetables and spoon sauce over the top.