Preheat grill to 450+ . You really want the grill to be super hot before you add your peaches.
Slice peaches in half. The two halves should easily separate. Using a spoon scoop out the pit of the peach. Alternatively, you could use a paring knife.
Brush the peach halves with melted butter or olive oil and add flat side down to the grill. Cook for about 1-2 min and remove. The peaches should be very ripe already so really don't need a lot of time on the grill.
Transfer to a plate. Slice in half and wrap in a slice of prosciutto. Add them all to a large plate and drizzle everything with balsamic glaze. Top with fresh chopped basil. Enjoy!