In a medium mixing bowl, whisk together the all-purpose flour, baking powder, and salt until evenly combined. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat the unsalted butter and granulated sugar on medium-high speed until the mixture is light and fluffy, approximately 2 minutes.

Add the large egg and vanilla extract to the butter mixture. Beat on medium speed until fully incorporated.

Reduce the mixer speed to low and gradually add the flour mixture. Continue mixing until a smooth dough forms.

Remove half of the dough from the mixing bowl and wrap it in plastic wrap; set aside. To the remaining dough in the mixer, add the peppermint extract, finely ground peppermint candies, and red food coloring. Mix on low speed until the ingredients are fully combined and the dough is evenly tinted.

Place the peppermint dough between two sheets of parchment paper. Roll it into a rectangle approximately 14 inches by 8 inches. Chill in the refrigerator for 15 minutes. Repeat this process with the reserved plain dough.

After chilling, carefully place the peppermint dough layer on top of the plain dough layer, aligning the edges. Gently press to adhere the layers together. With the long side facing you, tightly roll the dough into a log shape. Wrap the dough log in plastic wrap and refrigerate until firm, at least 2 hours.

Preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper.

Using a sharp knife, slice the chilled dough log into ¼-inch thick rounds. Arrange the cookie slices on the prepared baking sheets, spacing them 1 inch apart.

Bake the cookies in the preheated oven for 12 to 14 minutes, rotating and switching the baking sheets halfway through, until the edges are just beginning to turn golden.

Allow the cookies to cool on the baking sheets for 10 minutes before transferring them to a wire rack to cool completely. Repeat with any remaining dough.