How to Make It
Preheat the oven to 350°. In a large enameled cast-iron casserole, heat the oil over moderately high heat. Season the lamb shanks with salt and pepper. Add them in batches to the casserole and cook until browned, about 5 minutes per side; transfer to a platter. Add the carrots, onion, chopped garlic, tomato paste and rosemary to the casserole and cook, stirring, until fragrant, about 3 minutes.
Return the shanks to the casserole and add the wine and stock. Cover and bring the liquid to a boil, then cook the lamb stew in the oven, turning once, for about 2 1/2 hours, or until very tender.
While the lamb is cooking, make the polenta: in a large saucepan, bring 4 cups of water to a boil. In a bowl, combine the cornmeal with 4 cups of warm water. Whisk 1 teaspoon of salt and the cornmeal mixture into the saucepan until the mixture begins to thicken. Reduce the heat to low and cook, whisking vigorously every 5 minutes or so, until thick and creamy, about 1 hour. Remove from the heat and stir in 2 tablespoons of the butter and 1/4 cup of the Parmesan. Season with salt and pepper, cover and keep warm.
Melt the remaining 1 tablespoon butter. In a bowl, combine the butter, bread crumbs, shallot, parsley, minced garlic and the remaining 1/4 cup of Parmesan. Season with salt and pepper.
Increase the oven temperature to 400°. Spoon the polenta onto a large ovenproof platter and set the lamb shanks on top. Ladle 1/4 cup of the cooking broth over each shank. Pat each with 1/4 cup of the Parmesan crumbs. Arrange the vegetables around the shanks. Bake on the top shelf of the oven for about 15 minutes, or until the crumbs are browned. Garnish with the rosemary and serve. Pass the broth separately.