Rinse shanks and pat dry. Sprinkle lightly all over with salt and pepper, and place in a 12- by 17-inch roasting pan. Bake, uncovered, in a 450° regular or convection oven until meat is beginning to brown, about 20 minutes. With tongs, turn shanks. Add garlic, onion, and carrots to pan around shanks, mix to coat with fat in pan, and spread level. Bake until shanks are well browned and vegetables are beginning to brown, about 20 minutes longer.
Add wine, tomatoes and their juices, anchovies, thyme, savory, and orange peel to pan; stir carefully to mix and scrape browned bits free. Cover pan tightly with foil.
Bake in a 325° regular or convection oven until meat is very tender when pierced, 2 to 2 1/2 hours.
Uncover pan. Spoon off and discard fat from sauce. Gently stir artichoke hearts and olives into sauce around shanks and bake until heated through, about 10 minutes longer.
With tongs, transfer shanks to a rimmed platter or plates; pour sauce over lamb. Add salt and pepper to taste.