Preheat oven to 375°F (190°C).

Place eggplant slices on a baking sheet, brush with olive oil, and bake for 20 minutes until softened. Set aside.

In a large skillet, heat olive oil over medium heat. Add onion and garlic, cook until softened.

Add ground meat, cook until browned. Stir in crushed tomatoes, tomato paste, red wine, cinnamon, nutmeg, salt, and pepper. Simmer for 20 minutes, then stir in parsley. Remove from heat.

In a saucepan, melt butter over medium heat. Stir in flour until smooth. Gradually add milk, stirring constantly until thickened. Stir in nutmeg and Parmesan cheese. Remove from heat and stir in beaten egg.

In a greased baking dish, layer half of the eggplant slices. Top with meat sauce, then layer with remaining eggplant slices. Pour over the milk mixture.

Bake uncovered for 45 minutes or until golden brown and bubbly.

Let stand for 10 minutes before serving.