Cut the eggplants into slices about 1 cm thick. Sprinkle with salt and drain in a colander for about 20 minutes.
Peel the potatoes and also cut into 1 cm slices.
Rinse the salt off the eggplants and dry the slices well. Heat a layer of olive oil in a pan and fry the eggplant slices brown and tender on 2 sides. Drain the slices on kitchen paper.
Then fry the potato slices in the same way.
Chop the onion and finely chop the garlic. In another pan, heat some olive oil and sauté onion gently. When the onion is translucent, add the minced meat along with cinnamon and oregano and fry until brown. Add the tomatoes, sugar and bay leaf and bring to a gentle boil. Simmer gently over low heat for 20 to 30 minutes. Season to taste with salt and pepper.
Heat the oven to 180°C.
Make the béchamel sauce by melting butter in a saucepan. Add flour and stir well. Let cook for a few minutes until it slides through the pan like a cooked mass. Add the milk in 5 parts. Make sure it is well incorporated before adding the new amount. Keep stirring well so there are no lumps in the sauce. Simmer for a few more minutes until it is a thick sauce and remove the pan from the heat. Stir in nutmeg and 2/3 of the cheese and season with salt and pepper. Let cool for a few minutes, then stir in the egg yolk.
Grease a baking dish with oil. Lay the potato slices on the bottom with half of the eggplant on top. Pour the meat sauce on top, followed by the rest of the eggplant slices.
Pour the béchamel sauce on top and spread evenly. Sprinkle with panko and the rest of the cheese.
Bake for 30-45 minutes until the top is golden brown.