Preheat a skillet or grill pan over medium heat.
Spread unsalted butter evenly on one side of each slice of bread.
Place one slice of bread, buttered side down, onto the skillet.
Top with mozzarella cheese slices.
Cover with the second slice of bread, buttered side up.
Grill for 3 to 4 minutes until the bread is golden brown with visible grill marks.
Carefully flip the sandwich and grill the other side for another 3 to 4 minutes, until golden brown and the cheese is melted and gooey.
Remove from heat and let rest for 1 minute.
Cut the sandwich diagonally into two halves and stack slightly offset on a white ceramic plate.