Peel the eggplants and cut them into long pieces with a thickness of 1/2″ (1 cm). Sprinkle with salt, allow 20-30 minutes to drain the bitterness, wash them and dry them.
Roll them in a little flour and fry them until browned in preheated oil. Arrange them in a container and pour a mixture of pressed garlic, olive oil and salt over them. Then place them in a container with garlic and olive oil.
Wash the potatoes and put them to boil until semi cooked, then peel and cut them into circles. Cut the zucchini into circles too. Put an eggplant layer in an oiled dish, overlapping the ends, then a layer of potatoes, processed cheese and a third layer of zucchini, overlapping the same way.
Between the layers, sprinkle salt, black pepper, white pepper and slices of butter. Top with processed cheese and pour the beaten eggs and milk over the gratin. Put it to bake in a preheated moderate oven for about 25-30 minutes.
It can be served either hot or cold.