Once the pan is warm, add 1 piece of bread, buttered side down, and top with cheese and peach slices. Cover with a few arugula leaves, if using. Allow to cook until golden brown and crisp, about 3 to 4 minutes.
Close the sandwich with another slice of bread, buttered side up, then flip and cook until bread is toasted and cheese is melted, another 4 to 5 minutes.
Cut the sandwich in half and serve immediately.