Season lamb shanks with salt and pepper.
Heat olive oil in a Dutch oven; brown lamb on all sides, then set aside.
In the same pot, sauté carrots, onions, and garlic until softened.
Return lamb to pot; pour in red wine and simmer for 10 minutes.
Add tomatoes (with juice), chicken and beef broths, rosemary, and thyme.
Bring to a gentle boil, then cover and transfer to preheated oven.
Braise at 325°F (165°C) for 2.5 hours until meat is fork-tender.
Serve hot with mashed potatoes or rustic bread.