Rinse and dry fresh basil leaves, removing thick stems. In a food processor, combine basil, grated Parmesan, pine nuts, and garlic. Pulse until chopped, then drizzle in olive oil while blending until smooth. Season with salt and pepper, then set aside.

Spread a layer of basil pesto on one side of each bread slice. Layer fresh mozzarella, sliced tomatoes, and basil leaves. Drizzle with balsamic glaze if desired, then top with remaining bread slices.

Heat a panini press or skillet over medium heat. Spread butter or brush olive oil on the outer sides of the sandwich. Grill for 3-4 minutes per side, until the bread is golden and cheese melts.

Remove the sandwich from heat and let sit for one minute before slicing. Serve warm, optionally with chips or salad.