Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, cocoa, and salt in a bowl, stirring with a whisk.
Place butter and granulated sugar in a medium bowl. Beat with a mixer at medium speed 3 minutes or until light and fluffy. Add egg whites and vanilla; beat 1 minute or until well combined. Add flour mixture; beat at low speed just until combined. Spoon dough onto a 12-inch-long sheet of plastic wrap; gently press mixture into a ball. Wrap and chill dough for 1 hour.
Divide dough in half. Working with 1 portion at a time, roll dough to 1/4-inch thickness on a lightly floured surface; cut into desired shapes with 2 1/4- to 3 1/4-inch cookie cutters (wrap and refrigerate remaining dough portion to keep it chilled). Place cookies on baking sheets lined with parchment paper. Bake at 350° for 10 minutes or until cookies are firm in the center. Cool 2 minutes on pan. Remove cookies from pan, and cool completely on a wire rack.
Combine powdered sugar and remaining ingredients in a small bowl; stir with a whisk until smooth. Scrape icing into a heavy-duty zip-top plastic bag. Snip a tiny hole in 1 corner of bag with scissors; decorate cookies as desired with icing.