Put butter in heatproof 8-inch square pan and set over low heat until melted. Add sugar and mix until well blended. Arrange peach halves, cut side down, in sugar mixture. Prepare gingerbread mix according to package directions and pour over peaches. Bake in preheated 375° oven about 30 minutes, then loosen edges. Turn out on a serving plate, fruit side up, and cut in 2-inch squares. Top with whipped cream or Cool Whip.