Place melon cubes, lemon juice, white sugar, honey, and a pinch of salt in a blender and puree for 1 minute. Then add the mint and yogurt and puree another 1 minute. While pureeing, add the grappa. Transfer the puree to a glass pitcher. Refrigerate. Serve with crostini bread sticks wrapped in prosciutto to enhance the soup's sweet flavors.
Recipe courtesy Michael Chiarello