Stir together yogurt, schnapps and vanilla in a measuring cup. Combine peaches and sugar in a food processor; pulse until finely chopped. With the machine running, gradually pour yogurt mixture through the feed tube. Process until smooth and creamy, scraping down the sides of the bowl once or twice. Scoop frozen yogurt into chilled dessert dishes.
Make Ahead Tip: Cover and freeze for up to 4 days. Let soften in the refrigerator for about 20 minutes before serving.