Preheat the oven to 350. Line two baking sheets with parchment or silicone liners.
In a large bowl or the bowl of a stand mixer, beat together the butter, brown sugar, and sugar until smooth. Add the egg, egg yolk, and peppermint extract, and mix until combined.
In a small bowl, whisk together the flour, cocoa powder, baking soda, and salt. Add the dry ingredients to the wet ingredients, and mix until combined. Gently fold in the chocolate chips and peppermint baking chips.
Scoop the dough into one inch balls, then divide the balls in half and stack the two halves on top of each other like a snowman.
Bake 11-13 minutes, or until the cookies look dry on top and are very lightly browned around the edges. Let cool five minutes before removing to a cooling rack.