Peel eggplant and slice thinly (about 1/4 " thick). Saute slices individually in olive oil until the eggplant becomes translucent. Drain and put eggplant aside. Saute mushrooms and onions until the mushrooms stop giving off moisture. Drain. In an ovenproof casserole (fairly deep), pour a little olive oil just to grease the bottom of the dish. Add a layer of eggplant, onions & mushrooms, and mozzarella. Cover with sauce. Sprinkle parmesean on top. Repeat these layers until the dish is full. Top with last of sauce and parmesean. I usually have 2 or 3 layers depending on which dish I use. Bake at 350 for 45 minutes.