Grilling peaches deepens their natural sweetness, and when they're paired with prosciutto and basil, it's an unbeatable flavor trifecta: sweet, smoky, salty. That said, grilled peaches also pair well with vanilla ice cream.
Preheat grill to medium-high. Brush grill and peaches with oil. Season peaches to taste with salt and pepper. Grill, turning occasionally until charred and softened, 4 to 6 minutes. Transfer to a platter. Sprinkle with basil, grind pepper over top, and drizzle with oil. Serve with prosciutto on the side.