How to Make It
Preheat broiler with oven rack 6 inches from heat. Combine mayonnaise, onion, dill, banana peppers, capers, mustard, lemon juice, vinegar, and black pepper in a medium bowl. Fold in tuna.
Spread butter evenly on 1 side of each bread slice, and broil until toasted and golden brown, about 1 minute.
Divide tuna mixture on non-toasted sides of 2 bread slices; top evenly with pickles and 2 cheese slices. Broil until cheese is melted, 1 to 2 minutes. Top with remaining bread slices, toasted side up.