Place the wire rack in an oven with the “top grill” function at a distance of 10 cm from the top heating element. Turn on the oven to preheat to a high temperature.
In a medium bowl, combine the tuna, tomatoes, red onions, olives, dill, vinegar, oil, anchovy fillets, 1/4 teaspoon salt, and a little black pepper, and stir.
Put the slices of bread on a wire rack and place them under a preheated grill for 30-50 seconds, fry until golden brown. Then turn the slices of bread and put the tuna mixture on the unfried side, sprinkle with chopped cheese, and place the tuna sandwiches under the grill until the cheese melts about 1-2 minutes. Serve the tuna sandwiches right away.