Step 1Cut the honeydew in half. Cut each half into quarters and cut away the rind. Cut the honeydew into cubes (you'll need about 7 cups).
Step 2Puree the honeydew in a blender until smooth, working in batches if necessary. Pour the puree into a bowl. Stir in the mint and wine.
Step 3Divide the soup among 6 chilled bowls and top with a dollop of yogurt. Serve the soup by placing the bowls onto plates lined with crushed ice, setting the bowls into the ice.