In small bowl, whisk 2 cups of the flour, the baking powder and salt. In large bowl, beat butter and sugar until smooth, 1 minute. Beat in egg, egg white and peppermint. On low, beat in flour mixture. Remove half of dough to bowl; stir in remaining 1 tablespoon flour and tint dough pink with red food coloring. Knead cocoa into second half of dough. Flatten each piece into 8-inch disk; wrap each in plastic. Refrigerate 2 hours.

Heat oven to 350 degrees F. On floured surface, roll out chocolate dough to a 10 x 8-inch rectangle. Cut lengthwise into sixteen 1/2-inch-wide strips. Cut each strip in half crosswise; you will have 32 strips, each 5 x 1/2 inch. Roll under hands to make 6-inch ropes. Repeat with pink dough.

Twist together one chocolate rope and one pink rope. Curl a "hook" in one end of each twist, to form a candy-cane shape. Transfer to an ungreased baking sheet. Brush with beaten egg white.

Bake cookies at 350 degrees F for 8 to 10 minutes, until firm and golden around edges. Remove promptly from baking sheet; transfer carefully to cooling racks with large spatula. Cool completely.