Prepare your bechamel sauce and set aside.Melt butter in a saucepan over very low heat. Add salt, pepper and nutmeg.Add half the sifted flour and whisk well for 5 minutes.Pour in the milk little by little while whisking and gradually add the rest of the sifted flour. Continue whisking until the sauce becomes smooth, creamy and lump-free. Cut the tomatoes into small pieces and put them in a pan without oil. Let them cook until a lot of water evaporates, about 10 minutes. Then add a tablespoon of olive oil, the cinnamon and the chili pepper. Add salt and pepper and cook for another 5 minutes on low heat. Reserve also.
Cut the eggplants into 1 cm slices and brush them with olive oil on both sides, using a kitchen brush.
Place oiled slices in a hot skillet until golden brown. Cook longer to ensure they are well toasted. Set aside on a plate.
In the same pan, fry the chopped onions and pressed garlic with a little olive oil. Then add the minced meat and brown it. Then add the tomato sauce.
Preheat your oven to 180°C.
In a baking dish, alternate layers of eggplant and tomato sauce.
Finally, pour the béchamel sauce over the top of the gratin and sprinkle with grated cheese. Bake for 20 minutes until golden brown.