Preheat a skillet or grill pan over medium heat.
Spread unsalted butter evenly on one side of each slice of white bread.
Place one slice of bread, buttered side down, onto the skillet.
Layer the mozzarella cheese slices evenly on top of the bread in the skillet.
Cover with the second slice of bread, buttered side up.
Grill the sandwich for about 3-4 minutes until the bread is golden brown and crispy.
Carefully flip the sandwich and grill the other side for another 3-4 minutes until golden brown and the cheese is melted.
Remove from heat and place the sandwich on a plain white plate.
Cut the sandwich diagonally into two halves and stack them slightly offset.
Serve immediately while the exterior is crispy and the interior is gooey and melted.