Start your grill on smoke with the lid open until a fire is established in the burn pot (3-7 minutes). Preheat to 400°F. Combine brown sugar and cinnamon in a small bowl. Brush peach halves with melted butter. Once your is preheated, place the peach halves cut side down on the grates. Grill for 5-7 minutes, or until grill marks begin to form. Flip peaches over and sprinkled cinnamon sugar. Grill until the sugar mixture begins to caramelize, another 2-3 minutes. Serve hot.