In a heavy-bottomed skillet (I use cast iron), melt butter and a splash of olive oil on medium heat. Sprinkle sugar on the cut side of each peach half and fry, cut side down, leaving it in place for about 5 minutes until it becomes caramelized. (If you prefer to do this on the grill, oil the grill and close the lid.) When the peaches are browned, not burned, flip them over to the skin side, put the heat on low, and cook them covered for 5 to 10 minutes until softened. Check them at 5 minutes to be sure they are not burning. When they’re done, set them aside.