1. Arrange eggplant slices in a single layer on kitchen cloth or paper towels; sprinkle with salt.
2. Heat 1 tablespoon of the oil in a large skillet; cook lamb, stirring, until lightly browned. Spoon off excess fat. Mix in onion; cook, stirring occasionally, until onion is tender, 4 minutes. Mix in garlic, parsley, tomato paste, salt, cinnamon, oregano, nutmeg and pepper; stir in the wine. Heat to a boil; reduce heat to a simmer. Cover; cook 15 minutes. Uncover; simmer until sauce is thick, about 5 minutes.
3. For cream sauce, melt butter in a medium saucepan over medium heat; stir in flour, salt, pepper and nutmeg. Gradually stir in milk. Cook, stirring, until thickened, about 2 minutes. Beat eggs and egg yolk in a small bowl. Mix in a little of the hot sauce. Blend egg mixture gradually into sauce; cook, stirring, over low heat 2 minutes. Remove from heat; cover. Keep warm.
4. Blot moisture from eggplant slices with paper towels. Arrange eggplant in a single layer on a baking sheet. Lightly brush with half of the remaining oil. Broil in oven, about 4 inches from heat, until lightly browned, about 5 minutes. Turn; brush opposite sides with oil. Broil until browned, about 5 minutes. Remove from oven; reduce oven heat to 350 degrees.
5. Place half of the eggplant in a single layer in an ungreased 2-quart square or oval baking dish. Top with meat sauce; sprinkle with 2 tablespoons of the Parmesan cheese. Cover with remaining eggplant; sprinkle with 2 tablespoons of the cheese. Pour on cream sauce; sprinkle with remaining cheese. Bake until top is lightly browned, 45 minutes-1 hour.