Preheat oven to 400 degrees. Lightly brush both sides of each bread slice with oil. Season with salt and pepper. Transfer to a rimmed baking sheet. Toast in oven until pale golden, about 7 minutes per side. Transfer sheet to a wire rack; let crostini cool completely.
Divide basil leaves and folded slices of prosciutto among crostini. Drizzle with oil. Season with pepper.