Rinse and pat dry eggplants, cut into 1 cm (approximately 1/2 inch) thick slices.
Peel onion and chop finely, cut potatoes into 0.5 cm (approximately 1/5 inch) thick slices.
Rinse bell peppers, halve and remove seeds and ribs, dice. Heat 1 tablespoon of butter in a pan and saute diced peppers for a few minutes, add 1/2 cup of water and season with salt and pepper. Simmer, covered, for about 7 minutes. Remove from heat and puree.
Prepare bechamel sauce. Heat butter in a saucepan, add flour and cook until light brown. Add milk and cream and simmer for about 5 minutes, stirring occasionally. Season with salt, pepper, sugar, lemon juice and zest. Remove from heat and cool.
Heat 3 tablespoons of oil in a large skillet, brown ground beef and onions until crumbly. Add pepper puree and chopped parsley; season with salt, pepper and cinnamon. Heat remaining oil in another pan and cook eggplant slices until browned on both sides, season with salt and pepper. Line large, greased baking dish with half of potatoes slices, season with salt and pepper and spread some of bechamel sauce on top. Spread with eggplant slices and cover with remaining potatoes. Drizzle wtih a little bechamel sauce and spread ground beef mixture evenly on top. Whisk remaining bechamel sauce with eggs and pour over meat. Bake in preheated oven at 180°C (approximately 350°F) for about 40 minutes. Remove from oven and serve.