Combine 2 cups powdered sugar, corn syrup, water, peppermint and shortening.
Mix at low speed (use the paddle attachment on your mixer) just until the mixture comes together.
Transfer ⅓ of mixture to a separate bowl and add red food coloring and mix until the color is uniform.
Dust work surface with powdered sugar and knead white mixture until smooth.
Roll out white mixture between sheets of parchment or wax paper until ⅛-1/4″ thick.
Knead red mixture on work surface until smooth.
Roll out red between sheets of parchment or wax paper until ⅛″ thick.
Place both rolled peppermints in freezer for 15 minutes.
Using a 1″ cookie cutter, cut out as many white circles as possible and place them on a parchment lined sheet.
Using then same cookie cutter, cut out half as many red circles as you have white circles and place 1 white circle on on top of each white circle. Top with another white circle.
Place in freezer for at least 40 minutes.
Melt chips by microwaving for 45 seconds, stirring and repeating until melted and smooth.
Place each patty on fork and dip in chocolate. Gently tap against side of bowl to let excess drip off.
Place patty back on sheet.
Refrigerate 10 minutes to let chocolate set up.
Place white chocolate in the corner of a zippered sandwich bag and microwave for 45 seconds.
Knead chocolate to make sure it is melted. If not, microwave another 15 seconds.
Clip very tip of corner, and pipe a snowflake design on mints