Lay the slices of eggplant on paper towels, sprinkle lightly with salt, and set aside for 30 minutes to draw out the moisture. Then in a large skillet over high heat, sprinkled with olive oil, quickly fry the eggplant in batches until browned. Set aside on paper towels to drain.
In the same large skillet over medium heat, melt the butter and add the ground beef, salt and pepper to taste, onions, and garlic. After the beef is browned, sprinkle in the cinnamon, nutmeg, fines herbs and parsley. Pour in the tomato sauce and wine, and mix well. Simmer for 20 minutes. Allow to cool, and then stir in beaten egg.
To make the béchamel sauce, begin by scalding the milk in a saucepan. Melt the butter in a large skillet over medium heat. Whisk in flour until smooth. Lower heat; gradually pour in the hot milk, whisking constantly until it thickens. Season with salt, and white pepper.
Preheat oven to 350 degrees. Layer half of eggplant in a greased 9x13 inch baking dish. Cover the eggplant with all of the meat mixture, and then sprinkle 1/2 cup of Parmesan cheese over the meat. Cover with remaining eggplant, and sprinkle another 1/2 cup of cheese on top. Pour the béchamel sauce over the top, and sprinkle with the nutmeg. Sprinkle with the remaining cheese.
Place the baking dish on a baking sheet lined with foil to catch any spills. Bake for 1 hour. Cool slightly before serving