Wash the eggplants and cut them into round slices. Put them in salted water to soak for about 15 min. and get rid of the bitterness. Rinse and dry them. Marinate them with olive oil.
Heat a grill pan and grill the eggplant slices. Peel the tomatoes and grate them coarsely.
Put 2-3 tbsp olive oil at the bottom of a suitable oven dish. Distribute the grated tomatoes on top. Arrange a layer of grilled eggplants on top of the tomatoes.
On top of each eggplant slice, place a round slice of processed cheese, then another eggplant on top of it. Bake in a preheated oven for about 20 min.
Take the oven dish out and sprinkle the eggplants generously with grated cheese. Finish baking until the cheese is ready. Sprinkle the ready dish with pressed garlic and finely chopped dill. Serve warm.