In a medium skillet over medium heat, add the butter and let it bubble for a bit. Add the bread and toast on one side until golden brown.
Meanwhile, slice the tomato and fresh mozzarella into ½” slices.
When the first side of bread is toasted, flip it and add the tomatoes and mozzarella. Stack the basil leaves on top. Place the second piece of bread grilled side-down on top of the mozzarella. Grill until cheese melts and bread is toasted.