Place the eggplant and zucchini in a colander. Sprinkle with salt. Let sit for 20 minutes. Pat dry with paper towel.
Fry eggplant in one frying pan and zucchini in another, with olive oil in each pan. Fry until soft on the inside and brown on the outside. Remove fried vegetables with a slotted spoon. Let them drain on paper towels.
Using one of the frying pans, fry potatoes in oil until soft. Drain on paper towels.
Sauté hamburger and onion in ½ cup olive oil for 10 minutes. Stir in wine, salt and pepper, cinnamon stick, tomato paste, bay leaf, water, and allspice. Simmer for 20 minutes. Take out cinnamon stick and bay leaf. Add the grated cheese. Mix well.
Preheat oven to 350⁰ F.
In a large, lightly greased lasagna pan, layer ½ of the potatoes, ½ the eggplant, ½ the zucchini, and all of the meat mixture. Repeat with ½ the potatoes, ½ the eggplant and ½ the zucchini.
Top with béchamel cream and cook in the oven for 40 minutes. Let it cool for 20 minutes before serving.
For the Béchamel Cream, in a bowl, mix ½ cup of cool milk with the flour, egg, salt, and pepper.
Bring 2 ½ cups of milk to a boil. Add the butter and then add the flour/milk mixture. Stir continuously until mixture thickens. Remove from heat and use to top Moussaka.