Heat grill to medium-high.
In a cast iron skillet over the grill, combine the pitted cherries, sugar, red wine, and balsamic vinegar. Bring to a simmer and cook, stirring occasionally, until the fruit is soft, 6 to 8 minutes. Transfer the mixture to a food processor and puree until completely smooth. Return the mixture to the skillet over medium-high heat. Add the cherry liqueur and simmer until reduced to about 1/4 cup, 1 to 2 minutes.
Cut the peaches in half and remove and discard the pits. Place the halves in a medium bowl. In a small saucepan set over low heat, melt the butter and brown sugar together. Coat the peaches with the butter mixture. Grill the peaches over direct medium heat until grill marks are clearly visible and the peaches are soft, 10 to 12 minutes, turning once halfway through grilling time. While the peaches are still warm, layer each serving glass with 2 peach halves, 1 scoop of ice cream, and 1 tablespoon of cherry sauce. Tuck a couple of benne wafers into each glass and serve immediately.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.