Place bread on a cutting board and spread mayonnaise over top side of each.
Heat a small skillet over medium. Slide in half of butter. When it melts, place 1 slice of bread, mayonnaise side down, in skillet; top with half of the cheese; season with pepper. Then add the turkey and cranberry relish. Top with the rest of the cheese. Top with second slice of bread, mayonnaise side up.
When underside is golden brown, about 4 minutes, turn sandwich and add remaining butter to skillet. Press down on sandwich to encourage even browning and to help melt cheese—be gentle, don’t smash it. Cook until second side is golden brown and cheese is melted.