Preheat the oven to 350 degrees F.
Cream 10 tablespoons of the butter with the sugars in a medium bowl, and then beat in the vanilla and egg yolk. Add the flour and cocoa and beat until smooth. Transfer the dough to wax paper and roll into a 10-by-2-inch log. Wrap and refrigerate 1 hour.
Slice the dough into 1/4-inch rounds and flatten gently on a baking sheet. Bake 7 to 8 minutes, and then let cool 10 minutes.
Meanwhile, cream the remaining 4 tablespoons butter with the confectioners' sugar, peppermint extract and 1 teaspoon of the cream until smooth. Spread about 2 teaspoons of peppermint cream each over half of the cookies and close with a plain baked cookie.
Melt the chocolate chips with the remaining cream in a small saucepan, adding more cream to make it smooth but not runny. Spread over half of the cookies and top with the candy canes while the chocolate is still wet.
Recipe courtesy Devon Delaney