Heat a large skillet (or panini press) to medium heat. Butter the bread slices and flip over. Lay a slice of cheese on four pieces of bread.
Then slice 4 thin apple rounds, close to the core. Lay them on top of the cheese slices. Spread 2 tablespoons of pimento cheese on top of the apple and top with the remaining slices of bread, butter-side-up.
Grill the sandwiches 3-5 minutes per side, or 3-5 minutes total in a panini press.