Prepare the Pesto: In a food processor, blend fresh basil, Parmesan cheese, pine nuts, garlic, olive oil, salt, and black pepper until smooth.
Assemble Sandwiches: Spread mayonnaise on one side of four slices of bread. On the other side, layer pesto and two slices of cheese. Top with remaining bread slices.
Grill: Heat a skillet over medium heat. Spread butter on the outside of each sandwich and grill for 3-4 minutes per side until golden brown and cheese is melted.
Serve: Let sandwiches rest for a minute before slicing and enjoy warm with your favorite sides.