Place eggplant slices on baking sheets coated with cooking spray and sprinkle with salt. Bake at 450 until tender and somewhat brown (about 7 minutes, flipping them halfway).
Meanwhile heat olive oil, onions and garlic in a skillet on medium heat. After 5 minutes, add mushrooms, tomatoes, chickpeas, cinnamon, all spice and red wine. Put the lid on and let simmer for 10 minutes.
In a 13x9 dish, place on layer of eggplant on the bottom, then spoon half the tomato mixture on top. Repeat layers. There will probably be liquid left in the pan, but that's okay. Just discard it because the flavors are distributed in the veg mixture. However, you may want to reduce the liquid and pour if over the dish. It will just take more time.
Mix together the yogurt, egg, egg whites, nutmeg and cheese. It won't be completely smooth. Season with salt and pepper to your liking and pour over the tomato mixture.
Bake at 350 for about 40 minutes, or until the top looks set.