Preheat oven to 350 F. In a large mixing bowl, combine eggs, milk or water, cheese, salt and pepper; set aside. Heat olive oil or butter in a large skillet; saute onions and any optional vegetables desired until vegetables are tender. Add vegetables and sausage to egg mixture; stir well.
Place 12 foil baking cups into cupcake pan. Distribute sausage and egg mixture evenly into baking cups. Bake for 22 minutes or until eggs are set. Remove from oven. Sprinkle with Parmesan if desired.