1. Stack cheese slices; cut into quarters. Trim ham slices to fit bread. Top 12 bread slices with 1 slice cheese, 2 slices ham and another slice cheese. Top with remaining bread slices. Spread outsides of sandwiches with butter. (This step can be done up to 4 hours ahead. Cover; chill.)
2. Warm a skillet over medium heat until hot. Cook sandwiches in batches, for 1 to 2 minutes; flip and cook other side until bread is toasted and cheese has melted. Let rest on a work surface for 1 minute; cut in half on the diagonal. Serve warm with pickle chips and mustard for dipping, if desired.