Wash the eggplants. Remove the base of the stalk and cut lengthways in 3/8 inch/ 1 cm slices. Place the slices in a bowl, cover with water, sprinkle with salt, and leave to draw for 20 minutes. Meantime, peel the potatoes, cut into similar 3/8 inch/ 1 cm slices, and add salt. Drain the eggplants and pat dry. Heat the olive oil in a pan and brown the eggplant on both sides over a high heat (you will have to keep adding oil). Remove the slices from the pan and place on paper towels to drain. Put fresh olive oil in the pan, and fry and drain the potato slices in the same way. Sauté the onions until transparent, add the ground meat and brown over a high heat. Stir in the tomatoes, white wine, sugar, cinnamon, and parsley, reduce the temperature, and simmer for 10 minutes. Melt the butter in a pan, stir in the flour, and cook for a minute or two. Slowly pour in the milk, stirring continuously. When the mixture thickens, remove the pan from the heat, stir in the egg yolk, and season the sauce with sugar, nutmeg, lemon, salt, and pepper. Stir in 2 tbsp of the grated graviéra and allow to cool.
Preheat the oven to 350 °F (180 °C). Cover the base of a large ovenproof dish first with a layer of potato slices, then half the ground meat mixture. Next come the eggplant slices, then the remaining ground meat. Pour over the bechamel sauce, smooth over the top, and sprinkle with breadcrumbs, cheese, and if desired, with cinnamon. Cook in the preheated oven for about 45-60 minutes, until the top is golden brown. Allow the finished dish to cool a little before cutting into large portions for serving. Serve with freshly baked white bread.