Pat lamb shanks dry and trim off any excess fat.
Season well with salt and pepper.
Het olive oil in large, heavy pan until shimmery.
Working in batches, cook lamb shanks until brown on all sides, about 8 minutes. Transfer shanks to plate and set aside.
Add onions, carrots and garlic to pot and sautee until golden brown, about 10 minutes.
Stir in wine, tomatoes, chicken broth and beef broth.
Season with rosemary and thyme. Return shanks to pot, pressing down to submerge.
Bring to a boil, then reduce heat to medium-low.
Cover, and simmer until meat is tender, about 2 hours.
Remove cover from pot. Simmer about 20 minutes longer.
Transfer shanks to platter, place in a warm oven.
Boil juices in pot until thickened, about 15 minutes. Spoon over shanks to serve.