Preheat the oven to 350 F. In a medium bowl, whisk together flour, cocoa powder, salt, and baking soda. In another large bowl, combine softened butter with sugar until fluffy.
Add in egg and peppermint extract, and mix until smooth. Add in the flour mixture, and mix until a thick dough forms.
Place the powdered sugar into a shallow dish. Roll the cookie dough into balls, and roll into the powdered sugar. Place at least 2-inches apart onto ungreased baking sheets. Bake for 10-12 minutes.