Slice the peach all the way around the pit lengthwise. Separate peach into 2 halves and remove the pit. Sprinkle ½ tablespoon brown sugar on each half of peach. Let sit for 10 minutes. Preheat grill and make sure grates are well oiled. Place peaches cut side down on grill and cook until lightly caramelized, and there are nice grill marks. Place 1 peach half in a bowl, and put 1 teaspoon of butter in the middle of each peach, and top with 1 scoop of ice cream.