Heat grill to high. Grill peach wedges, flipping, until caramelized, about 1 to 2 minutes per side. Careful to not burn them.
Preheat oven to 400 F degrees.
Sprinkle cheese on pita breads and top with prosciutto. Bake until cheese melts and is bubbling, about 8 minutes. Remove from oven and top with peaches, basil and green onions. Top with chopped pecans for an extra crunch. Drizzle with oil.