Season lamb shanks with salt and pepper, then sear them in a large Dutch oven with olive oil over medium-high heat until deeply browned on all sides; remove and set aside.

In the same pot, sauté chopped onion, carrots, and celery until softened, then stir in minced garlic and cook for one minute until fragrant.

Deglaze the pot by pouring in red wine, scraping up any browned bits, and bring to a simmer to reduce slightly.

Return the lamb shanks to the pot, add beef broth, diced tomatoes, rosemary, thyme, and bay leaves, then bring the liquid to a gentle simmer.

Cover the Dutch oven tightly and transfer to a preheated 325°F (160°C) oven, braising for 2.5 to 3 hours until the lamb is fork-tender.

Carefully remove shanks, allow them to rest, then skim excess fat from the sauce, adjust seasoning, and serve with the rich braising liquid.