Preheat the oven to 375° and line a baking sheet with parchment paper. On a work surface, fold each slice of prosciutto in half lengthwise to form a thin strip. Place a persimmon wedge at one end of each strip and roll it up in the prosciutto. Using a toothpick, poke a hole in the wrapped persimmon and slip in a sprig of rosemary. Place the wrapped wedges on the baking sheet and brush them lightly with olive oil. Roast for about 20 minutes, until the prosciutto-wrapped persimmons are lightly browned and sizzling. Serve warm or at room temperature.