1. Preheat grill to 350° to 400° (medium-high) heat. Sprinkle chicken with salt and pepper. Grill chicken, covered with grill lid, 7 to 10 minutes on each side or until done. Let stand 10 minutes, and cut into slices.
2. Stir together mayonnaise and next 2 ingredients. Spread mixture on 1 side of each bread slice. Top 4 bread slices with chicken, Gouda, and next 2 ingredients. Top with remaining bread slices, mayonnaise mixture sides down. Brush sandwiches with melted butter.
3. Cook sandwiches, in batches, in a preheated panini press 2 to 3 minutes or until golden brown.