Preheat broiler. Melt butter in heavy 10-inch nonstick skillet over medium heat. Add mushrooms and saute until golden brown, about 8 minutes. Beat eggs and green onions to blend in bowl. Season with salt and pepper. Pour egg mixture over mushrooms and stir briefly. Let eggs begin to set around edges. Lift edges and tilt pan, letting uncooked portion flow under cooked eggs. Cook until eggs are almost set but still slightly moist, about 30 seconds. Arrange cheese slices atop frittata. Broil until cheese melts and bubbles. Slide frittata onto plate and serve.