Place peaches in a 1 gallon plastic freezer bag and freeze until solid (about 24 hours).
Submerge frozen bags in very hot tap water for 1 minute. Open and pour any thawed syrup into food processor bowl. Remove fruit from bag; carefully cut into chunks, about 2 inches in size.
Place into food processor with remaining ingredients (blender or mini-processors are not recommended). Process until smooth, scraping blade as needed.
Serve immediately or freeze until ready to serve. Garnish with additional Peach Slices and fresh mint, if desired.