Preheat oven to 375 degrees.
Break the sugar cookie dough put in a large bowl. Add the unsweetened cocoa and mix well.
Scoop level tablespoons of the dough, roll into balls, and coat in granulated sugar.
Bake in a well greased mini muffin pan for 11-13 minutes.
Allow the cookie cups to cool before removing them from the pan.
Cut or break the curves off of the mini candy canes. Save the remaining pieces for crushing or for other baking. (Making the candy cane handles is difficult, so you can use pretzel handles instead if you prefer.)
Melt the white chocolate chips in the microwave (re-melt them as necessary). Dip the ends of the candy cane handles in the melted white chocolate chips and attach to the cookie cups by holding them in place for 30-60 seconds or until they stay. (skip the handles if this is to labor intensive for you)
Bring the heavy cream just to a boil in the microwave and then mix in the powdered hot chocolate mix. Add the semi-sweet chocolate chips. Let sit for about 3 minutes and then stir until smooth. Mix in the peppermint extract.
Spoon the peppermint ganache into the cookie cups.
Top with crushed candy canes and mini marshmallows.
Store in the refrigerator.