Cut the eggplants lengthwise into slices no thicker than 5 mm, lay them out on a board or plate, add salt and leave for 20 minutes to remove the bitterness. Then rinse and dry.
Fry each eggplant slice in oil for 3-5 minutes on each side or bake them in the oven.
Finely chop the tomatoes and onions, crush the garlic with a knife or a special press. Grate the cheese on a large grater and set it aside for now.
Fry the onion in a frying pan for 1-2 minutes, then add the tomatoes and garlic. Stir-fry for 5-7 minutes until the vegetables are soft.
Add spices to the vegetables, stir, remove from heat and transfer to a deep container. Grind the dressing with a blender until it reaches the consistency of a sauce.
Place the minced meat in a greased, heated frying pan and fry until the meat changes color from pinkish-red to brown.
Add the vegetable dressing to the minced meat, stir and simmer for another 5 minutes.
Melt the butter in a saucepan, add the flour and pour in the warm milk. Mix thoroughly without removing from the heat until the sauce becomes uniform in consistency.
Grease a baking dish with milk sauce and place a layer of fried eggplant on top.
Place a layer of minced meat on the eggplants and sprinkle with grated cheese.
Repeat all layers again: milk sauce, eggplant, minced meat, cheese. Bake the dish in the oven, preheated to 180 ℃, for 30-40 minutes.