For the eggplant: Wash eggplant and cut off both ends. Peel 1/2-inch strips of peel from the eggplant, making stripes of skin. Slice crosswise into 1/3-inch rounds. Salt and pepper both sides and let stand for 30 minutes. Rinse and dry. Heat the oil in a large saute pan, and fry the eggplant on both sides, until golden brown. Drain well on paper towels.
Preheat oven to 350 degrees F.
For the Meat Filling: Heat the butter in a large skillet. Add the onions and cook until tender, 3 to 4 minutes. Add the beef and cook until brown, about 6 minutes. Add the wine and reduce until it is almost dry. Add in tomato paste, water, parsley, salt, pepper, and cinnamon. Simmer for 30 minutes, remove from heat and cool.
For the bechamel: In a medium saucepan, melt the butter. Blend in the flour, and gradually stir in the milk. Cook, stirring, until thick and smooth. Add in the nutmeg, salt and pepper. Cool. Add 4 ounces of cheese and blend well. For the assembly: Butter a 9 by 12 by 2-inch baking dish. Arrange half of the eggplant and half of the meat mixture, alternately, until completely used. Cover with the bechamel sauce, and the remaining cheese. Place in the oven and bake for 40 minutes. Remove to a rack and let cool for 20 minutes. Cut into 3-inch squares and serve warm.