In the bowl of a stand mixer, beat the butter for one minute. Add the sugars, and beat together on medium-high speed until creamy. Beat in the egg, followed by the vanilla and peppermint extracts until just combined.
Whisk together the dry ingredients in a separate bowl (flour, cocoa powder, baking soda, and salt). Slowly beat the dry ingredients into the wet ingredients a half a cup at a time. Fold in the mint chocolate chips with a spatula. Cover the bowl with plastic wrap and chill in the fridge for at least two hours, or up to overnight.
Once the cookies are chilled, heat the oven to 350°F and prepare a baking sheet with parchment paper. Fill a small bowl with the confectioner's sugar. Set out the dough for 20 minutes, then scoop out balls (about 1-2 tablespoons each) and roll them in the confectioner's sugar. Arrange the sugar-coated balls of dough on the prepared baking sheets and bake for 8-9 minutes. Remove from the oven, allow to sit for 5 minutes, and then transfer to a cooling rack. Cookies keep fresh at room temperature in a sealed container for up to a week, or can be frozen for up to 3 months.