Spread 1 tablespoon of pesto on one side of each slice of bread.
On two of the bread slices with the pesto side up, layer mozzarella or place fresh mozzarella on top. Sprinkle grated Parmesan if desired, then top with remaining bread slices, pesto side down.
Spread a thin layer of softened butter on the outside of each sandwich.
Preheat a non-stick skillet over medium heat and grill the sandwiches for about 2-3 minutes on each side until golden brown and the cheese is melted.
Remove from skillet, slice in half, and serve immediately while warm.