Season the lamb shanks with salt and pepper. Heat olive oil in a large ovenproof pot over medium-high heat. Add lamb shanks and brown on all sides, about 2-3 minutes per side. Remove shanks and set aside.

Reduce heat to medium. Add onions and garlic to the pot, cooking until softened, about 5 minutes. Add carrots and celery; cook for an additional 5 minutes.

Stir in tomato paste and cook for 1 minute. Return lamb shanks to the pot. Add beef broth, rosemary, thyme, and bay leaves. Bring to a simmer.

Cover and transfer to a preheated oven at 325°F (163°C). Braise for 2 to 2.5 hours, or until the meat is tender and falls off the bone.

Remove bay leaves and herb stems before serving. Season with salt and pepper to taste.