Heat oven to 400°F. Cut eggplant into 1/3-inch disks, sprinkle with salt; let sit in a colander for about 30 minutes or until eggplant releases water. Rinse well, pat dry and brush each side with olive oil. Place on baking pan; roast until golden, about 20-30 minutes.
In a large saute pan, heat oil and cook onion on medium-high heat for 3 to 4 minutes, add garlic, reduce heat to medium-low and saute for 8 to 10 minutes until onions are tender. Add lamb, increase heat to medium-high, stirring often, about 15 minutes; drain. Add remaining ingredients. Stir, cover, and simmer on medium-low heat for 20 minutes.
Bechamal (white) Sauce:
In a small pot, melt butter. Whisk in flour; cook for 2 to 3 minutes on medium heat, stirring often. Whisk in milk, one cup at a time; bring to a boil, stirring constantly. Simmer on low for an additional 2 minutes. Remove from heat; add nutmeg, 2 tablespoons cheese, salt and pepper; set aside.
Heat oven to 350°F. Divide eggplant slices into three stacks. In a 9-by-13-inch baking pan, place one layer of eggplant. Add half the meat sauce. Repeat with second layer of eggplant and remaining meat sauce. Add the third layer of eggplant. Whisk the egg into the bechamal sauce until smooth. Spread sauce over the final eggplant layer. Top with remaining cheese; bake for 50 to 60 minutes, until golden. Let stand 10 minutes before serving. Serves 8.
Tip: Salting the eggplant before cooking helps to remove the bitter flavor.
Approximate Nutrient Analysis per serving:
550 calories, 40 g fat, 17 g saturated fat, 125 mg cholesterol, 600 mg sodium, 25 g carbohydrate, 7 g fiber, 12 g sugar, 26 g protein