To assemble: Butter one side of each slice of bread. Place 4 slices on your work surface, buttered side down. Place a slice of ham on each bread slice, folding it to fit if necessary. Top with 4 to 5 apple slices per sandwich, followed by the cheese. Place the remaining 4 bread slices on top, buttered side up. (If the sandwich seems quite thick, press it down to compress the ingredients slightly.)

STOVETOP METHOD: Heat a large nonstick skillet over medium-high heat for 2 minutes.

Put the sandwiches in the skillet (in batches if necessary), cover, and cook for 2 minutes, or until the undersides are golden brown and the cheese has begun to melt.

Uncover, and turn the sandwiches with a spatula, pressing firmly to flatten them slightly. Cook for 1 minute, or until the undersides are golden brown.

Turn the sandwiches again, press with the spatula, and cook for 30 seconds, or until the cheese has melted completely. Serve immediately.

SANDWICH MAKER METHOD: Preheat the sandwich maker. Follow directions for sandwich assembly, and cook according to the manufacturer's instructions.

GAS GRILL METHOD: Brush the grill rack with oil and preheat the grill to medium-high. Follow directions for sandwich assembly. Put the sandwiches on the grill and follow directions for the stovetop method.