Cut the melanzane lengthwise with salt and put them in a colander to lose water.
Fry the melanzane in oil.
In a frying pan, saute the onion and garlic in olive oil until soft. Then saute the mince while mixing constantly. Add the tomatoes and sugar and season with salt/pepper. When the sauce thickens, remove from heat and cool. Add parsley and egg white. Butter an ovenproof glass baking dish (about 22×35) and top with 2 tablespoons rusk crumbs. Cover the first layer with melanzane, then minced meat sauce and top with half of the cheese and 2 tablespoons of rusk crumbs. Do the same with the second layer. At this point you can freeze the Mussaka (it will keep for a couple of months).
Mix the béchamel with the whipped cream and the 3 eggs and pour it over the mussaka after beating it briefly.
Roast in the oven at 200 degrees for about 40 minutes.