Position rack in center of oven and preheat to 325Â°F. Heat 1 tablespoon reserved oil in heavy large pot or Dutch oven over high heat. Season lamb shanks lightly with salt and pepper. Add lamb to pot and cook until brown, turning frequently, about 6 minutes. Add garlic and stir 1 minute. Add canned tomatoes, broth and sun-dried tomatoes. Bring liquids to boil. Cover pot and bake lamb until almost tender, turning once, about 1 hour. Add artichoke hearts. Cover and bake until lamb is very tender, about 20 minutes. (Can be prepared up to 1 day ahead. Cool, cover and refrigerate.)
Transfer lamb to plate. Spoon fat from surface of pan juices. Boil pan juices over high heat until slightly thickened, about 5 minutes. Season to taste with salt and pepper. Return lamb to pot and rewarm over low heat.
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