Preheat oven to 375 degrees. Salt eggplant well, arrange in colanders, and place weighted bowls on top. Let drain for 30 minutes. Rinse and dry.
Heat oil in a large skillet over medium heat. Add onion, 1 teaspoon salt, and 3/4 teaspoon black pepper; cook until tender, 7 to 10 minutes. Add oregano, cinnamon, cumin, and cayenne; cook 2 minutes more. Add lamb, and cook until it browns, about 5 minutes. Drain fat from pan. Break up tomatoes, and add to pan. Cook over medium heat, stirring often, until sauce starts to thicken, about 8 minutes.
Place 4 eggplant slices in an 8-inch square baking pan, and top with a third of the sauce. Repeat twice, making four three-layer stacks. Combine 1 teaspoon parsley and breadcrumbs; sprinkle over the top.
Cover with foil, and bake for 1 hour. Remove foil, and bake for 10 to 15 minutes more. Sprinkle with remaining parsley; serve hot.