In a large bowl, whisk together flour, baking powder and salt. In the bowl of a stand mixer with the paddle attachment or in a large bowl using an electric hand mixer, beat butter and granulated sugar on medium speed until light and fluffy, about 2 minutes. Beat in egg, egg yolk, vanilla extract and peppermint extract until just combined. Gradually stir in flour mixture just until a dough forms.

Remove half of the dough and transfer to empty flour mixture bowl. Add red food coloring to stand mixer or large bowl with remaining dough; stir on low speed just until food coloring is fully incorporated, about 1 minute.

Shape each half of dough into a rectangular block about 8x2x2 inches. Wrap each block tightly in plastic wrap. Refrigerate at least 1 hour or up to 3 days.

On a cutting board, slice each block lengthwise into 3 equal-sized strips. Slice each strip lengthwise into thirds to make 9 total long, thin strips of dough (about 1/3-inch thick) per block.

Line up a strip of red dough, white dough and a second strip of red dough on cutting board; press strips together to seal edges. Top with 3 more strips of dough in alternating colors; press to seal. Repeat with a third and final layer. Trim off and discard any rounded edges. Repeat with remaining 9 strips of dough, beginning and ending with white dough, so you end up with two blocks of checkerboarded dough.

Tightly wrap blocks in plastic wrap and refrigerate for at least 1 hour or up to 1 day.

Preheat oven to 350°F. Line two baking sheets with parchment paper and arrange two oven racks in upper and lower thirds of oven.

If desired, roll ends of dough blocks in colored sugars. Use a sharp knife to slice each block of dough into 1/4-inch slices (you should end up with about 32 cookies total); arrange on prepared baking sheets spaced at least 1 inch apart. Bake, rotating baking sheets halfway through baking, until cookies are set in centers, about 12 to 14 minutes. Let cookies cool on baking sheets for 5 minutes, then transfer to a cooling rack to cool completely.

Store leftover cookies in an airtight container for up to 1 week.