Preheat your galley over to 400º or as hot as you can get it.
Cut eggplant into 1/4-1/2" slices. Sprinkle with salt on both sides and sweat in a colander for 30 minutes.
After 30 minutes of sweating, pat the eggplants dry with paper towels. Brush both sides with EVOO, lay on a roasting pan or cookie sheet and roast in your hot oven for about 20 minutes. You will have to do this in at least two batches. If they have not browned after about 20 minutes, light your broiler for 5 minutes. Once all the eggplants have roasted, turn your oven down to 350º.
While the eggplants are roasting, prepare the meat sauce. Heat 1 tablespoon EVOO in a large fry pan or pot. Add the chopped onions and garlic, Sauté until onions start to soften. Add the ground beef and ground lamb. Cook until meat is browned. Once browned, add the canned tomatoes, tomato paste, parsley, white wine, cinnamon and sugar. Simmer for 30 minutes. Adjust seasonings with salt and pepper.
Grease a 13x9" casserole (cake pan size) and place one layer of roasted eggplant on the bottom of the pan. Spoon on half of the tomato-meat sauce. Repeat with another layer of eggplant, then the rest of the meat sauce on top.
BÉCHAMEL
In the same large pot melt the butter, add the flour and cook for 2 minutes. Add the milk and cook, stirring constantly until the sauce thickens. Add the nutmeg, 1/4 cup parmesan, salt and pepper. Take off the burner and let cool down a bit so it’s no longer hot. You don’t want the eggs to cook when you add them.
Once the sauce has cooled down whip in the 4 beaten eggs. Pour the sauce evenly over the top of the meat sauce. Sprinkle with the remaining parmesan cheese.
Bake in the 350º preheated over for 1 hours, until golden on top. Remove from the oven and let rest for at least 10 minutes before serving.