Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, cocoa, and baking soda in a small bowl, stirring well with a whisk.
Combine the brown sugar and next 5 ingredients (brown sugar through peppermint extract) in a medium bowl; beat with a mixer at high speed for 2 minutes. Beat in the egg white. Add flour mixture; beat at low speed until well-blended.
Coat your hands lightly with cooking spray. Shape the dough into a 6-inch log. Wrap log in plastic wrap; freeze 1 hour or until firm.
Preheat oven to 350°.
Cut the log into 24 (1/4-inch) slices, and place 1 inch apart on baking sheets lightly coated with cooking spray. Bake at 350° for 10 minutes. Remove from pans; cool on wire racks.