Preheat oven to 450°.
Place flatbreads on two baking sheets and drizzle each with 1 Tbsp. olive oil.
Place 3 Galbani thick Mozzarella slices per bread, layer with peach slices, prosciutto, and 1/8 cup basil per bread, then season with salt and pepper.
Bake until crust is crisp and golden and cheese is melted, about 8 minutes.
Remove from oven and sprinkle with additional basil, to your liking.
Cut each pizza into quarters and serve immediately.