Preheat your oven to 375F. Line to large sheet pans with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and granulated sugar until light and fluffy— about 2 minutes on medium-high speed. Make sure to scrape down the sides of the bowl 1-2 times.
With the mixer on low, add the egg and vanilla extract. Mix just until combined.
Next, with the mixer on low, add the flour and cocoa powder. Mix just until no large lumps of dry ingredients remain.
Lastly, add the chocolate chunks and peppermint chips. Fold them into the dough with a silicone spatula.
Scoop the cookies onto the parchment lined baking sheets.
Bake for 12-14 minutes, or until the cookies are set in the center.
Store the cookies in an airtight container at room temperature for up to 5 days.