Mix together 2 cups of the powdered sugar, corn syrup, water, peppermint and shortening, at low speed until it comes together.
Put ⅓ of the mixture in a bowl and mix food coloring into it until evenly colored.
Sprinkle confectionery sugar over work surface and knead the larger dough until smooth.
Roll the dough out between sheets of parchment or wax paper until approximately ⅛-1/4" thick.
Now knead the colored dough on the work surface and roll out until about ⅛" thick.
Place both rolled peppermint doughs in freezer for 10-15 minutes to stiffen.
Line a tray or baking sheet with waxed paper.
Now cut out as many circles as you can from each rolled dough. Place white circles on wax paper and top each with a colored circle.
Place in freezer for about 45 minutes.
Melt the dark chocolate chips by microwaving for 40 seconds, stirring and repeating in 20 second interments until smooth.
Place each patty on a fork and dip into chocolate. Gently tap against side of the bowl to let the excess chocolate drip off, then place back on the waxed paper.
Place in a cool spot until chocolate has firmed up.
Melt the white chips, and pour into the corner of a zipper sandwich bag and snip off a small piece of the corner to pipe the white chocolate.
Pipe out a snowflake or other decoration on top of the peppermint patties.