1. In a medium mixing bowl beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add the 3/4 cup sugar, the baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg, milk, vanilla, and peppermint extract. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.
2. Divide dough in half. Stir red or green paste food coloring into half of the dough. If necessary, cover and chill dough for 30 to 60 minutes or until dough is easy to handle.
3. Divide each half into 6 pieces. Roll each piece into a 12-inch-long rope. Lay ropes side by side on a lightly floured surface, alternating colors. With a rolling pin, roll assembled ropes into about a 14x9-inch rectangle that is 1/4 inch thick. Using a pastry cutter, pizza wheel, or long sharp knife, cut the rectangle diagonally into 1/2-inch-wide strips. Cut strips into pieces about 5 to 7 inches long. (Press shorter strips together end to end to reach desired length.) Place on an ungreased cookie sheet. Curve one end of each piece to form a candy cane. If desired, sprinkle lightly with additional sugar.
4. Bake in a 375 degree F oven for 7 to 8 minutes or until edges are firm and bottoms are very lightly browned. Transfer cookies to a wire rack; cool. Makes about 36 cookies.
Nutrition facts per cookie: 74 cal., 4 g total fat (2 g sat. fat), 10 mg chol., 33 mg sodium, 99 g carbo., 0 g fiber, 1g pro.