Cut the eggplants and potatoes into thick slices, then cut each slice in half. Finely chop the onion, garlic, and red bell pepper. Place everything in a large pot with the olive oil. Sauté over heat.

Once the potatoes and eggplants are well sautéed, add the ground beef and continue to sauté. Add salt, pepper, and your chosen spices. Finally, add the grated tomatoes and tomato paste. Add a splash of water if needed.

Lower the heat and let it simmer. From this point on, don't use a spoon to stir; instead, gently shake the pot to mix. Let it simmer on very low heat until the potatoes and eggplants are tender and the liquid is absorbed.

Remove the pot from the heat and stir in one handful of grated Gruyère cheese. Mix gently. Pour the mixture into a baking dish (mine is 9.5 x 14 inches / 24 x 36 cm) and spread it out evenly. Sprinkle the other handful of Gruyère cheese on top.

Prepare the béchamel sauce. Heat the milk in a saucepan. In a small bowl, mix the flour and olive oil well until smooth. When the milk is hot, add the flour and oil mixture, stirring quickly. Continue stirring until it thickens. Remove from heat and add salt, pepper, nutmeg, and the grated cheese. Stir to combine.