Put the vinegar in a small saucepan and bring to a simmer over high heat. Cook until thick and syrupy, stir in the honey and season with salt and pepper, if using. Let cool slightly.
Brush the peach halves with oil and season with salt and pepper, if using. Place on the grill, cut side down and grill until golden brown. Turn over and grill for 1 minute longer. Remove the peaches from the grill and drizzle with the balsamic. Wrap or stuff each half with a slice of the prosciutto. Sprinkle the basil over the top and drizzle with olive oil.
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