In the bowl of a stand mixer, fitted with a paddle attachment, cream together the sugar and butter until fluffy, about 2-3 minutes. Scape down the sides and add in the egg and vanilla extract.
In a separate mixing bowl whisk together the flour, cocoa, baking powder, and salt. Slowly add the dry ingredients into the wet until incorporated.
Dust a clean working surface with cocoa powder, transfer the dough out onto the dusted surface. Divide into two manageable sections and roll each piece out, until it's 1/4" thick.
Using a circle cutter or a mason jar lid cut circles out of the dough, place on a cookie sheet lined with a baking mat or parchment paper. Place in the fridge to chill for at least 30 minutes, or up to a day.
Once the cookies have chilled, bake at 350 degrees F, for 8-10 minutes, allow the cookies to cool slightly on the baking sheet before transferring to a cooing rack. Allow to cool completely before coating.
In a microwave safe bowl combine the white chocolate chips, butter, and peppermint extract. Microwave in 30 second intervals until the mixture starts to melt. Than microwave in 15 second intervals until completely smooth. Add in the cream and stir to combine. Dip the cookies in the melted chocolate mixture, and allow to cool on a piece of wax or parchment paper. The cookies may need to be double coated, depending on the chocolate.
While the chocolate is still melted sprinkle the tops with crushed peppermints, allow to cool completely before packaging. These will keep in an airtight container for 4-6 days.
Notes
**You can dip in white, milk, or dark chocolate. If using different types of chocolate to melt, you will want to adjust the amounts needed. For example, if you want half white and half milk chocolate like I did, use 5 oz. of both white and milk chocolate, 1 tablespoon of butter each, 1 tablespoon of heavy cream each, and 1/2 tsp of peppermint extract per chocolate mixture!**You can also pour the chocolate over the cookies instead of dipping. Leave the cookies on the cooling rack and place on top of a sheet of wax or parchment paper and slowly pour the chocolate mixture over the top until all the cookies are evenly coated, again this may need a couple coats. Milk or dark chocolate coats much heavier than white chocolate. **Crush candy canes or peppermints in a Ziploc bag with a rolling pin or meat tenderizer! For a finer texture, pulse a few times in a blender or food processor - I prefer a finer consistency so I blended my peppermints in the blender.