Combine flour, cocoa, baking powder and salt in medium bowl until well mixed; set aside.
Combine powdered sugar and butter in large bowl. Beat at medium speed, scraping bowl often, until creamy. Add egg and peppermint extract; continue beating until well mixed. Reduce speed to low; gradually add flour mixture. Beat until well mixed.
Divide dough into thirds. Shape each into a ball; flatten slightly. Wrap each in plastic food wrap; refrigerate until firm (at least 2 hours or overnight).
Heat oven to 375°F. Roll out dough on lightly floured surface, one-third at a time (keeping remaining dough refrigerated), to 1/8-inch thickness. Cut with 2-inch round cookie cutter. Place 1 inch apart onto ungreased cookie sheets. Bake for 6 to 8 minutes or until set. Remove to wire cooling rack. Cool completely.
Place candy coating in small microwave-safe bowl; microwave on HIGH (100% power), stirring often, for 60 to 90 seconds. Stir until smooth.
Place waxed paper onto flat surface. Dip each cookie into warm coating; shake off excess. Place onto waxed paper. Immediately decorate as desired. Let stand until coating is set.
Store between layers of waxed paper in loosely covered container.