Wash the eggplants without removing their caps and cut each in half. Put each half with the light side down on a board and cut into 4-5 strips. Salt the thus cut eggplant fan liberally and place at an angle for 30 minutes to drain out its bitterness.
Then rinse and dry them. Cut the feta cheese and tomatoes into thin pieces. Between the strips of eggplants, put a piece of feta cheese and a tomato ring. Arrange the so prepared eggplants in a greased tray. Distribute the unpeeled cloves of garlic, and if you have any tomatoes left, chop them finely and distribute them in the tray.
Sprinkle again with a little salt, white pepper, savory and basil. Top with olive oil and cover the tray with foil. Pierce in several places for the steam to escape and set it to bake at 392°F (200 °C) in a pre-heated oven for about 40 minutes, or until the eggplants are ready.