1. Heat 1 tablespoon oil in large nonstick, ovenproof skillet. Cook onion and bell pepper 2 to 3 minutes. Add mushrooms; cover and cook 1 minute. Stir and cook 2 minutes more. Transfer to bowl.
2. Heat broiler. Whisk eggs, water, 3/4 cup of the cheese, the salt, and pepper in bowl. Heat remaining oil in skillet. Add egg mixture and basil and cook 1 minute; reduce heat to medium-low. Sprinkle mushrooms over eggs. Cover and cook 5 to 6 minutes, until just the edge is puffed. Sprinkle remaining cheese over top; broil 1 minute. Makes 4 servings.