In a medium 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 softened butter and sugar on medium-high speed until light and fluffy, about 2 minutes.

Add the egg and vanilla extract. Beat until fully incorporated, scraping down the sides of the bowl as needed.

Reduce the mixer speed to low. Gradually add the flour mixture and mix just until a soft dough forms.

Remove half of the dough from the mixing bowl and set it aside. This will be the plain vanilla dough.

To the remaining dough in the mixer bowl, add the peppermint extract, finely ground peppermint candies, and red food coloring. Mix until the peppermint dough is evenly colored and fully combined.

Place the peppermint dough between two sheets of parchment paper. Roll it into a 14 by 8-inch rectangle. Transfer the rolled dough to the refrigerator and chill until firm, about 15 minutes.

Repeat the same process with the reserved plain dough, rolling it between two sheets of parchment paper into a 14 by 8-inch rectangle. Chill until firm, about 15 minutes.

Once both dough layers are firm, place the peppermint dough on top of the plain dough. Gently press the layers together so they adhere.

With the long side facing you, carefully roll the layered dough into a tight log. Wrap the log securely in plastic wrap and refrigerate until firm, at least 2 hours.

Preheat the oven to 375°F. Line two baking sheets with parchment paper.

Remove the chilled dough log from the refrigerator. Slice the dough into 1/4-inch rounds using a sharp knife.

Place the sliced cookies on the prepared baking sheets, spacing them about 1 inch apart.

Bake for 12 to 14 minutes, switching and rotating the baking sheets halfway through baking, until the edges are just lightly golden.

Allow the cookies to cool on the baking sheets for 10 minutes, then transfer them to a wire rack to cool completely.

Repeat the slicing and baking process with any remaining dough.