1cup(2 sticks) unsalted butter, at room temperature
1 1/2teaspoonpure vanilla extract
1teaspoonred food coloring
Whisk flour, baking powder, and salt in a medium bowl.
Beat butter and sugar with an electric mixer on medium speed until light and fluffy, about 2 minutes. Add egg, egg yolk, and vanilla; beat on medium speed until combined, about 30 seconds. Gradually add flour mixture, beating on low speed until just combined, about 30 seconds. Transfer half of dough to empty flour mixture bowl.
Add peppermint and food coloring to dough in mixer. Beat on low speed until just combined and no streaks remain, about 1 minute.
Shape each section of dough into a long rectangular block about 8 inches long, 2 inches wide, and 2 inches high. Wrap tightly in plastic wrap. Refrigerate until cold and firm, at least 1 hour and up to 3 days.
Slice each dough block length-wise into 3 equal strips on a cutting board, then slice each strip lengthwise into thirds to make 9 long, thin strips (about 1/3 inch thick) per block.
Line up a strip of pink dough, a strip of white dough, and a second strip of pink dough on cutting board. Gently press strips together. Top with 3 more strips in alternating colors. Repeat for a third layer. Trim off and discard any rounded edges. Repeat with remaining 9 strips, beginning and ending with white dough, to make a second block of checkerboard dough.
Rewrap checkerboard dough blocks and refrigerate until cold and firm, at least 1 hour and up to 1 day.
Preheat oven to 350°F with racks in upper and lower thirds of oven. Slice each dough block into 1/4-inch-thick squares. Arrange on baking sheets lined with parchment paper, leaving 1 inch between each cookie. Bake until set in center, about 12 minutes. Let cool on baking sheets for 5 minutes, then transfer to a wire rack to cool completely, about 30 minutes. Store in an airtight container for up to 5 days.