Position a rack in the middle of the oven, and preheat the broiler. Line a baking sheet with aluminum foil.
Gently toss the peaches with 1 tablespoon olive oil on the prepared baking sheet; season with salt and pepper to taste and arrange cut-side down.
Broil until the skins are slightly charred, about 5 minutes. Turn so the skin side is down, and continue to broil until the tops of the peaches are lightly browned, about 5 minutes more. Drizzle lightly with olive oil, and cool slightly.
Sprinkle the warm peaches with the mint, and wrap a piece of prosciutto around each peach quarter. Drizzle with the balsamic vinegar, and top with a few grinds of pepper.
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