Prepare the glaze. Combine all of the ingredients for the glaze in a heavy saucepan and bring to a boil over high heat. Briskly simmer the glaze until thick and syrupy, 4 to 6 minutes. Remove the pan from the heat.
Set up your grill for direct grilling and preheat to high. If a light smoke flavor is desired, toss the hickory chips on the coals (if using a charcoal grill) or place in a smoker pouch (if using a gas grill).
Grill the peaches until nicely browned on both sides, 2 to 4 minutes per side, basting with the glaze. Transfer the peaches to plates or a platter and top with ice cream, if using. Spoon any remaining glaze over them. Garnish with mint sprigs and serve at once.