Combine butter, powdered sugar, and flour in a large bowl using an electric mixer (I use my stand mixer with a paddle attachment). The dough may appear crumbly, but keep mixing and it will turn into a soft dough. Trust me! You can also form the dough with your hands.
Roll dough out on a lightly floured surface using a rolling pin. The dough should be thin, about 1/4″ thick.
Cut out using a cookie cutter and place on an ungreased cookie sheet lined with parchment paper.
Bake at 325 degrees for 14 minutes*. Let cool on a baking sheet for 5 minutes before transferring to a wire rack. Cool completely.*The edges and bottoms of the cookies should be a light golden brown. I cook these cookies a little longer than normal so that they are nice and set up. Perfect for dipping. While the cookies cool, go ahead and get your melted chocolate ready.
Melt Andes baking chips in a microwave-safe bowl for 60 seconds. It won’t be completely melted, but warm. Stir until everything is melted and smooth.
Dip cookies into the chocolate using a fork. Tap the fork against the side of the bowl to allow excess chocolate to drip off. Scrape the bottom of the fork against the side of the bowl to remove even more chocolate.
Place chocolate-covered cookies on a parchment paper-lined baking sheet.
Microwave white chocolate chips and shortening in a microwave-safe bowl for 30 seconds. Stir. Heat for an additional 20-30 seconds. Stir until everything is melted and smooth. Spoon melted white chocolate into a small ziploc baggie. Make a small cut in the corner then drizzle white chocolate over the chocolate-dipped cookies.
Sprinkle with crushed candy canes.