Rinse eggplant, cut off the ends, cut into slices and sprinkle with salt. Let stand one hour, then dab accumulate liquid with a paper towel. Saute the eggplant slices in hot oil on both sides until golden brown. Peel the onions, finely chop and sauté in 2 tablespoons hot butter until translucent, then add the ground lamb and cook, stirring frequently until crumbly and season with pepper, salt and cinnamon. Blanch the tomatoes for a few seconds, peel, quarter, core and chop. Add the chopped tomato, tomato paste, parsley, wine and sugar to the ground beef. Mix everything thoroughly and simmer about 15-20 minutes. In a baking dish greased with olive oil, arrange a layer of eggplant, cover with the the meat mixture, sprinkle with oregano and top with another layer of eggplant.
Heat the butter in a saucepan until foamy, stir in flour and cook slightly. Gradually stir in milk, bring to boil and let thicken, season with salt and pepper and simmer for 5 more minutes, stirring occasionally. Allow to cool slightly.
Beat the eggs and stir into the warm béchamel. Stir in half of the feta cheese and season with salt. Pour over the eggplant in the baking dish, sprinkle the remaining feta cheese over and bake in an oven preheated to 180°C (approximately 350°F) convection/ 220°C (approximately 400°F) convention about 45 minutes. Remove from oven and serve.