In a food processor or blender, process the peaches until finely shaved, scraping the bowl occasionally.
Add the yogurt, sugar, peach schnapps and vanilla extract and process 1 minute or until well combined and smooth, scraping the sides of the bowl if necessary.
Spoon into parfait glasses.
Notes
FOOD NOTE: If desired, substitute 1/2 cup skim milk for the schnapps. The result will be more like an ice milk with a creamier consistency.