Place anchovy fillets on a cutting board and sprinkle with ¼ teaspoon of the salt; smash and scrape them using the flat side of a knife until the mixture forms a smooth paste.
Stir together anchovy paste, mayonnaise, and garlic in a small bowl until combined; set aside.
Slice tomato into ½-inch-thick slices and sprinkle with pepper and remaining ¼ teaspoon salt.
Evenly spread anchovy mayonnaise over each bread slice.
Arrange seasoned tomatoes on each of 2 bread slices; top with remaining 2 bread slices, mayonnaise side down.
Cut each sandwich in half and serve immediately.
