Gather all ingredients.

Season lamb shanks with salt and pepper.

Heat oil in a large, heavy pot or Dutch oven over medium-high heat. Working in batches, cook lamb shanks until brown on all sides, about 8 minutes. Transfer shanks to a plate; set aside.

Add carrots, onions, and garlic to the pot and sauté over medium heat until golden brown, about 10 minutes.

Stir in wine, tomatoes, chicken broth, beef broth, rosemary, and thyme.

Return lamb shanks to the pot, nestling them into the braising liquid. Bring to a boil, then reduce heat to medium-low. Cover and simmer until lamb is tender, about 2 hours.

Remove the lid and simmer to allow flavors to concentrate, about 20 minutes. Transfer lamb shanks to a platter; cover with foil to keep warm. Continue boiling sauce until thickened, about 15 minutes.

Spoon sauce over lamb shanks before serving.