Brush each peach half generously with the melted butter. In a cast iron grill pan, over medium high heat, place the peach halves open side down. Grill for about 5 minutes, until the peaches get golden brown. Turn the peaches over and sprinkle the inside of the halves with the brown sugar. Continue to grill for about 5 minutes. You want the underside to also get lovely char marks and get golden brown.