In a baking dish about 14 inches in diameter, place a layer of potatoes and lightly salt. Sprinkle with grated cheese.

Continue with a layer of eggplants, lightly salt, and sprinkle with grated cheese.

Repeat with another layer of eggplants.

Remove the meat sauce from the heat and add a handful of grated cheese. Mix well.

Spread the meat sauce evenly over the eggplants.

Prepare the béchamel sauce in a non-stick or aluminum pot. Heat the butter and add all the flour at once. Stir quickly to combine into a paste.

Remove from heat and slowly add the milk, stirring constantly to absorb the milk without forming lumps. Although this process is usually done over heat, I find it much safer to do it off the heat.

Add a little salt, pepper, and nutmeg. Beat the eggs with a fork in a plate and slowly add to the cream, stirring continuously. Add a handful of grated cheese and mix.

Slowly pour the béchamel over the meat sauce.

Bake at 480°F (250°C) for about an hour. If it starts to brown too much on top, cover with aluminum foil.