Slice the eggplants lengthwise into evenly thick slices or use a vegetable slicer. Lightly fry them in a pan with some oil.
Sauté the onions in oil and add the pressed garlic. Once the onions are translucent, add the tomatoes and spices to taste. Bring to a boil and let it simmer for about 10 minutes. Then mix in the Creme Fraiche.
In a baking dish, layer lasagna sheets first, then pour the tomato sauce over them. Spread Creme Fraiche on top, place the eggplants, and sprinkle with cheese. Repeat these layers until either the dish is full or you run out of ingredients. Finish with a layer of sauce and cheese on top.
Let it sit for an hour to let the flavors meld or prepare it the night before and refrigerate. Bake at 180°C in a convection oven for about 40 minutes.