Heat a skillet or grill pan over medium heat.
Butter one side of each slice of bread evenly.
Place one slice of bread butter-side-down onto the pan.
Layer fresh mozzarella cheese on top of the bread in the pan.
Top with the second slice of bread, butter-side-up.
Grill the sandwich until the bread is golden brown and crisp, about 2-3 minutes.
Carefully flip the sandwich and grill the other side until golden and the mozzarella is melted, about 2-3 minutes more.
Remove from heat and let sit for a minute before cutting the sandwich diagonally into two halves.
Serve the halves stacked slightly offset on a white ceramic plate.