Cut the peaches in half and remove the pits. Dust the cut side of each half with some of the sugar and ginger. Light a charcoal grill and allow the coals to burn until well covered with gray ash or heat a gas grill to low. Place the peaches sugar side down on the center of the cooking grate. Grill 6 to 7 minutes or until golden brown. Remove from grill.
Grate the zest from the lime, then squeeze the juice. In a small bowl, combine the juice, zest, and honey.
Serve the peaches with a scoop of vanilla ice cream, drizzled with some of the sauce.