Preheat the oven according to cookie package directions. Bake cookies on parchment or silpat lined baking sheets according to package directions.
Allow the cookies to cool completely on wire cooling racks. While they are cooling, prepare a large sheet pan lined with parchment paper. You can also crush the candy canes. Place unwrapped candy canes in a plastic bag, seal it, and then hit it with a rolling pin until crushed. Once the cookies are completely cooled, you can dip them in the white chocolate.
Add the white chocolate chips and shortening (if desired, makes it easier/smoother) in a microwave safe bowl. Microwave in bursts of 15 seconds, stirring in between each burst for 10 seconds until the chocolate is melted and smooth.
Dip half of the completely cooled cookies in white chocolate mixture. Slide the bottom of the cookie against the edge of the bowl to get rid of excess chocolate and immediately transfer to a large sheet pan lined with parchment paper. (IF the white chocolate is getting hard to work with, just put it back in the microwave for 15-20 seconds)
Immediately, add the crushed peppermint to the melted white chocolate. Allow cookies to harden at room temperature.