Step 1In the bowl of a stand mixer, or in a large bowl using an electric mixer, cream together the butter and sugar until light and fluffy, 3 to 5 minutes. Beat in the egg yolk and vanilla until thoroughly combined.
Step 2In a separate bowl, whisk together the flour, baking powder and salt. Slowly beat the flour mixture into the butter mixture, or stir in the flour mixture by hand until evenly combined to form a dough.
Step 3Divide the dough in half, and add the food coloring and peppermint extract to one of the halves.
Step 4On a large work surface, roll each portion of dough between wax paper into a 16-by-10-inch rectangle. Remove the wax paper and place the red rectangle over the plain one, then roll up the dough lengthwise jelly-roll style. Wrap the roll in plastic wrap and refrigerate overnight, or until firm.
Step 5Heat the oven to 350 degrees. Unwrap the roll and cut it into one-fourth-inch-thick slices. Place the slices 2 inches apart on lightly greased baking sheets. Bake until set, 12 to 14 minutes. Cool 2 minutes before removing the cookies to a wire rack to cool completely.