Combine wine, Schnapps, sugar, mint, cinnamon, and nutmeg in a large pot; stir in half-and-half until sugar dissolves. Add peaches.

Cook over medium heat, stirring frequently until peaches are tender, about 15 minutes; reduce heat if necessary to prevent scorching. Cool slightly.

Transfer peach mixture to a blender or the bowl of a food processor; blend until smooth. Refrigerate, covered, until ready to serve.