Wash the eggplants, cut off the stalks and use a sharp knife to cut lengthwise into slices about 1 cm thick. Place them on a board, add salt and leave for 20-30 minutes. When they are covered in juice, rinse them and remove the moisture with a paper towel. Peel the onion and chop finely. Peel the garlic. Warm the milk. Pour boiling water over the tomatoes for 2-3 minutes, remove the skins and grate them on a coarse grater. Also grate the cheese on a coarse or medium grater and divide it into 3 equal parts.
Prepare the filling. Heat a little olive oil in a frying pan over high heat and add the onions. Reduce heat to medium, brown onion for 3-5 minutes. Then place the minced meat in the pan, stir and fry for about 3-5 minutes. Pour in white wine and chopped tomatoes. Simmer over low heat for 10-15 minutes. Add nutmeg, marjoram, salt and pepper, squeeze the garlic through a press. Stir and simmer, stirring occasionally, for approximately 5 minutes until the liquid has completely evaporated.
Prepare the eggplants. Lightly brush the eggplants on both sides with olive oil using a pastry brush. Then carefully place them on a wire rack and place in the oven for 3-5 minutes at 200 degrees.
Prepare the sauce. Place a saucepan or small saucepan over low heat. Place butter on the bottom and melt. Then add the flour and, stirring, fry for about 3 minutes until golden brown. Pour hot milk in a thin stream, constantly stirring with a whisk. When the sauce reaches the consistency of thick sour cream, add a third of the grated cheese, stirring constantly. Then add salt and pepper. Cook the sauce for 7-10 minutes until thickened.
Bake the moussaka. Grease a deep baking dish with olive oil. Carefully place the eggplants in the first layer and sprinkle them with one third of the grated cheese. Then add the meat filling. Add a third layer of sauce. Spread it over the entire surface and sprinkle with the remaining cheese. Place in the oven at 180 degrees for 45 minutes. After baking, let the moussaka cool at room temperature for 20 minutes to thicken the sauce - otherwise the casserole will be difficult to slice neatly.
Moussaka can be served either hot or cold as an independent dish. Garnish it with fresh basil before serving. White Greek wine goes perfectly with the dish.