Heat the grill to high. Grill peach wedges, flipping, until caramelized, about 2 minutes per side.
Preheat the oven to 400 degrees (or heat grill to medium). Sprinkle cheese on grilled pizza crusts.
Bake or grill, covered with lid, directly on grates, until cheese melts and is bubbling, about 8 minutes (time may vary slightly if grilling).
Remove from oven or grill. Top with peaches, prosciutto, and basil. Drizzle with oil. Can also drizzle balsamic glaze.