PREPARATION:

1. Combine flour, baking powder, salt and 1/2 cup cocoa in small bowl; set aside. Beat butter and granulated sugar in large bowl with electric mixer at medium speed 1 minute or until creamy. Add egg, 1 teaspoon vanilla and peppermint extract; beat until well blended. Gradually stir in flour mixture just until blended.
2. On lightly floured work surface, shape dough into 12X2-inch log. Wrap tightly in waxed paper, then wrap in plastic wrap. Freeze 2 hours or until firm.
3. Preheat oven to 350°F. Grease cookie sheets. Cut dough into 1/8-inch slices. Place slices 1 inch apart on prepared cookie sheets. Bake 9 minutes or until puffed and firm to the touch. Cool on cookie sheets 1 to 2 minutes. Transfer to wire rack to cool completely.
4. For icing, combine powdered sugar, hot water and remaining 3 teaspoons vanilla in medium bowl; stir until smooth. Add additional water, 1/2 teaspoon at a time, if necessary, until desired consistency is reached. Divide icing in half. Add remaining 1 tablespoon cocoa powder to one bowl; stir until well blended. Cover cocoa icing; set aside.
5. Frost cooled cookies with vanilla icing; let stand until set. Drizzle cookies with chocolate icing; let stand until set.