1Turn on the broiler and arrange a rack 6 inches below the element.
2In a small bowl, combine the tuna (including the oil it’s packed in), mayonnaise, mustard, capers and brine, and parsley. Using a fork, mix well to combine. In another small bowl, combine the cheeses.
3Lightly toast the bread on both sides. Evenly distribute the tuna salad on half the slices and sprinkle with the cheese mixture. Transfer the tuna-and-cheese-covered slices to a baking sheet and place under the broiler. Broil until the cheese is melted and bubbly, about 2 to 3 minutes.
4Top with the reserved toasted bread slices and serve.