Wash and dry eggplants, cut into circles, sprinkle with salt and let stay for 30 minutes. Cut tomatoes into circles, chop garlic.
Put eggplants in a layer on greased baking sheet, cover with a layer of tomatoes and garlic, sprinkle with salt and cover with mayonnaise.
Sprinkle vegetables with grated cheese and bake until crisp and golden. Serve cool or hot with chopped greens.