Boil the peeled potatoes in salted water without over-boiling. Cool them and cut into round slices. Cut the tomatoes and eggplants into round slices as well.
Bake the eggplants briefly in a grill pan. Saute the onions and garlic in a pan. Add the mince and after 3-4 min., remove from the stove.
Sprinkle with the chopped parsley and dill. In a buttered oven dish, start arranging the moussaka as follows: tomatoes (the round slices cut in 2), potatoes, mince, eggplants and so on until out of ingredients.
Sprinkle with a little salt on top. In a bowl, beat the eggs, pour in the cream and milk. Stir well and pour it over the moussaka. Bake the dish at 482°F (250 °C) for 30-35 min.