Preparation Heat 1 tablespoon oil in heavy wide pot over medium heat. Add leeks and garlic; sauté until leeks soften, about 5 minutes. Transfer leek mixture to small bowl. Sprinkle lamb shanks with salt and pepper; dust with flour to coat. Heat remaining 4 tablespoons oil in same pot over medium-high heat. Add lamb and cook until brown, turning occasionally, about 12 minutes. Add leek mixture, wine, tomatoes with puree, mushrooms, herbes de Provence, and carrots. Stir to coat lamb with vegetable mixture. Reduce heat to medium-low, cover, and simmer until lamb is very tender, turning twice, about 1 hour 30 minutes. Uncover and continue to simmer until sauce reduces slightly, about 10 minutes longer. Spoon off fat from pan juices. Season lamb to taste with salt and pepper. (Can be made 1 day ahead. Cool slightly. Chill uncovered until cold, then cover and keep refrigerated. Rewarm, covered, over low heat before serving.) Sprinkle with parsley and serve. Market tip:Not all supermarkets have lamb shanks on hand, so call ahead in case you need to order them.
Preparation Heat 1 tablespoon oil in heavy wide pot over medium heat. Add leeks and garlic; sauté until leeks soften, about 5 minutes. Transfer leek mixture to small bowl. Sprinkle lamb shanks with salt and pepper; dust with flour to coat. Heat remaining 4 tablespoons oil in same pot over medium-high heat. Add lamb and cook until brown, turning occasionally, about 12 minutes. Add leek mixture, wine, tomatoes with puree, mushrooms, herbes de Provence, and carrots. Stir to coat lamb with vegetable mixture. Reduce heat to medium-low, cover, and simmer until lamb is very tender, turning twice, about 1 hour 30 minutes. Uncover and continue to simmer until sauce reduces slightly, about 10 minutes longer. Spoon off fat from pan juices. Season lamb to taste with salt and pepper. (Can be made 1 day ahead. Cool slightly. Chill uncovered until cold, then cover and keep refrigerated. Rewarm, covered, over low heat before serving.) Sprinkle with parsley and serve. Market tip:Not all supermarkets have lamb shanks on hand, so call ahead in case you need to order them.