In a small bowl, whish 2 cups of the flour, the baking powder and salt. In a large bowl, beat butter and sugar until smooth, about 1 min. Beat in egg, egg white and peppermint. On low speed, beat in flour mixture. Remove half of dough to a bowl, tint dough darge pink, reddish with 6-8 drops of red food coloring. Knead 4 drops green food coloring into second half of dough. Flatten each piece into a 8-in disc, wrap each in plastic. Refrigerate 2 hours.
Heat oven to 350. On a floured surface, roll out dark pink dough to a 10x8 in rectangle. Cut lengthwise into 16 1/2 in strips. Cut each strip in half crosswise, you will have 32 strips, each 5 x 1/2 inch. Roll with hands to make 6-in ropes. Repeat with green dough.
Twist together one pink and one green rope. Curl one end of each twist into a hook to form a candy cane shape. Transfer to an ungreased baking sheet, brush with egg whtie, repeat.
Bake cookies at 350 for 8-10 min, until firm and golden around edges. Remove promptly from baking sheets, carefully transfer to wire racks to cool.
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