In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add the sugar, baking powder, and salt; beat until combined. Beat in the egg, vanilla, and, if desired peppermint extract until combined. Beat in as much of the flour as you can with the mixer. Stir in the remaining flour.
Divide dough in half. Tint one portion of the dough with paste food coloring. Knead coloring into dough until well mixed. If dough is too sticky to handle, wrap each half in waxed paper or plastic wrap and chill about 1 hour or until easy to handle.
On a lightly floured surface, roll each color of dough into a 12x8-inch rectangle. Using a large spatula and your hands, place one rectangle on top of the other. Press down gently with your hands to seal. Starting from a long side, tightly roll up jelly-roll style. Wrap the dough in waxed paper or plastic wrap. Chill at least 2 hours or until firm.
Using a sharp knife, cut log into 1/4-inch slices. Place slices about 1 inch apart on an ungreased cookie sheet. Bake in a 375 degree F oven for 8 to 10 minutes or until edges are firm and lightly browned.
Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; cool. Makes about 48 cookies.