Preheat your panini press or sandwich maker or nonstick skillet.
Arrange the bread slices on your cutting board. Place 1 slice of cheese on top of 2 of the bread slices; sprinkle the chopped piquillo peppers on top of the cheese. Top that with the 2 slices of ham, and finish it off with the last slices of cheese. Top with remaining bread -- no need for butter! Arrange the sandwiches in your sandwich maker or panini press; cook until the outside is golden brown and the cheese has melted. If using a nonstick skillet, once the sandwiches are in the pan, top with a piece of foil and then pop a tea kettle half filled with water on top of the foil. This will weigh the sandwiches down and give you that panini effect without a machine. If using a skillet, you'll have to flip the sandwiches.