Spread one side of each slice of bread with butter. Pile cheese onto two slices of bread and sandwich with remaining slices, buttered-side facing outward.
Press sandwiches in waffle iron until browned on outside and cheese is melted, about three to four minutes.
Meanwhile, thinly slice each avocado half and fan out to length of sandwich. Top each sandwich with sliced avocado and sprinkle with salt (if using).