Preheat oven to 350F.
Make the pasta frolla and put it in the refrigerator to rest.
Take one disc of dough out of the refrigerator and let it sit out until it is pliable. Once the dough is ready, put it on a well floured board, sprinkle some more flour over the top and roll it out to a 1/4 inch thickness.
Using your cookie cutters, cut out your shapes and place them on a baking sheet. Once you have no more room for another cutter, gather up your scraps of dough, roll out one more time, and cut out cookies. (Do not roll out more than twice.) Repeat the process for the second disc of dough.
As you fill up a baking sheet, put it in the oven and bake for 7-9 minutes for ~2 1/2 inch cookies. Mini cookies will take less time (my mini cutters take 5 minutes to bake) and large cookies might take more. When you take the baking sheets out of the oven, let the cookies rest for 1 minute, then transfer them to cooling racks.
When you are done baking cookies, make the chocolate topping.
Set a heat proof bowl over a medium saucepan. Fill the saucepan with 1-2 inches of water and bring it to a simmer. Add the chocolate chips and butter to the bowl. Stir occasionally with a silicone spatula. Once the chocolate is nearly melted move the bowl to a kitchen towel and keep stirring until the chocolate is completely smooth.
Either gently dip or spread the chocolate onto the cookies, keeping the chocolate to the top of the cookies. I like to spread the chocolate over the cookies with a spoon since the cookies are fairly tender and breakable.
As you top each cookie with chocolate, sprinkle it with some of the crushed candy canes and then place the cookie on a sheet of wax paper to set. Cookies will last up to 5 days if kept in a sealed container.