Spread the pesto onto one slice of bread, then top it with the mozzarella. Layer on the slices of prosciutto and add the basil leaves on top (if using). Add more cheese if desired, then top the sandwich with the other slice of bread.

Preheat a pan over medium heat. Spread a layer of mayonnaise onto the top of the sandwich, then place it onto the pan, mayo-side down (alternatively, grill the sandwich in butter). Spread another layer of mayonnaise onto the top of the sandwich, then once the bottom is golden-brown, flip it. Continue to cook a few minutes more, until the bottom of the sandwich is toasted. Transfer the sandwich to a plate and immediately.