Heat oven to 350 degrees F. Remove stems from mushrooms, chop and set aside. Remove black gills from inside of mushrooms. Heat oil in skillet and saute onions and chopped mushroom stems until tender. Add turkey. In a medium bowl, mix together spinach and eggs and add to turkey mixture. Add salt, pepper, basil and 1/4 C. Parmesan cheese. Stuff mushroom caps with mixture. Place in a shallow baking dish which has been sprayed with non-stick cooking spray. Sprinkle each with remaining Parmesan cheese, 1 T. per mushroom cap. Bake in 350 degrees oven for 15 minutes.