Step 1Heat a cast-iron pan or griddle over low heat. Brush one side of each bread slice with melted butter.
Step 2Spread half of the cheese evenly over the unbuttered side of two slices of the bread. Place a single layer of the pear slices over the cheese, then top with the remaining cheese. Place the remaining bread on top of each sandwich, buttered-side up.
Step 3With a spatula, place one of the sandwiches into the heated pan and weight it with a second heavy pan or a steak weight. (If your pan is large enough, cook both sandwiches; otherwise, cook them one at a time.) Cook until golden brown, about 3 to 4 minutes. Flip the sandwich, weight it with the pan or steak weight, and cook until golden brown, another 3 to 4 minutes.
Step 4Remove the sandwich to a cutting board and cut it in half or quarters. Serve immediately with a drizzle of chestnut honey, if desired, on the plate.