In a pot, heat about 2 inches of salted water (1/2 teaspoon salt to 1 cup water) and bring to a boil. Add brussel sprouts. Heat to boiling; reduce heat. Cover and cook until tender, 10-15 minutes and then drain. In a saucepan, cook and stir onion in butter and olive oil until tender. Pour over brussel sprouts and toss to coat well. Sprinkle with freshly grated parmesan cheese. Makes 4 servings.