In a medium bowl, combine mayonnaise, parsley, chives, tarragon, lemon zest, mustard, lemon juice, and black pepper. Add the broken pieces of tuna to this dressing, mix.
Put the fish mixture on 4 slices of bread, top with the tomato slices and sprinkle with cheese, cover with the remaining slices of bread. Grease the bread slices on the outside with softened butter.
Place the sandwiches on a baking sheet and bake the tuna sandwiches in the oven under the grill. Serve the tuna sandwiches hot.