Whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
Beat the butter and granulated sugar until light and fluffy, about 2 minutes. Add the egg, egg yolk, vanilla, and peppermint extract, and mix until combined.
Add the dry ingredients to the wet ingredients and mix just until combined.
Cover and refrigerate the dough for at least 2 hours, or overnight.
Heat the oven to 350°F and line a baking sheet with parchment paper. Roll the chilled dough into balls, then coat each in granulated sugar followed by powdered sugar.
Bake for 10 to 12 minutes, until puffed and cracked.
Cool on the baking sheet 5 minutes, then move to a wire rack.