Preheat the oven broiler. Line a cookie sheet with aluminum foil.
In a small bowl, make a paste with the butter, mayonnaise, garlic paste, basil, 2 tablespoons Parmesan, and pepper.
Spread equal amounts of the paste on each roll half. Arrange roll halves on the cookie sheet, topping side up, and sprinkle with remaining Parmesan cheese.
Broil on the top rack in the preheated oven 1 to 2 minutes, or until lightly toasted. Watch them very carefully! They can burn very quickly. Basically do these at the last minute before serving and check them closely as they broil.