Instructions

1. Place 2 sticks unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Let sit at room temperature until softened. Meanwhile, unwrap 5 candy canes and place in a large zip-top plastic bag. Smash with a rolling pin until finely crushed (about 1/3 cup).
2. Coarsely chop 4 ounces semisweet chocolate and place in a small microwave-safe bowl (no need to chop if using 2/3 cup chocolate chips). Microwave on high in 30-second bursts, stirring after each burst, until melted and smooth, about 1 1/2 minutes total.
3. Add 1 cup granulated sugar, 1 teaspoon vanilla extract, 1 teaspoon baking powder, and 1 teaspoon kosher salt to the butter. Beat with the paddle attachment on medium-high speed until lightened in color and fluffy, scraping down the bowl as needed with a flexible spatula, about 3 minutes.
4. Add 1 large egg and beat on medium speed until incorporated, scraping down the bowl as needed, about 1 minute. With the mixer on the lowest speed, add 2 1/4 cups all-purpose flour and beat until just a few streaks remain. Finish mixing by hand with a flexible spatula. Transfer half the dough (about 13 1/2 ounces) on a sheet of parchment paper.
5. Add 1 teaspoon peppermint extract, red food coloring of choice (10 drops gel or 25 drops regular), and the crushed candy canes to the remaining dough in the mixer. Beat on low speed until just combined, scraping the bowl about halfway through, about 1 minute total. Transfer the peppermint cookie dough to a second sheet of parchment paper.
6. If the mixer bowl has streaks of food coloring or candy cane residue in it, scrape it out with a flexible spatula or wipe it out with a paper towel. Return the first half of the dough to the mixer. Add the melted chocolate, 3 tablespoons black cocoa powder, and 1 large egg yolk. Mix on the lowest speed until just combined, stopping and scraping down the bowl halfway through, about 30 seconds total. Do not over mix. Return the dough to the sheet of parchment paper.
7. Shape the mint dough, still on its parchment paper, with your hands into a rough rectangle with a long side closer to you. Cover with a second sheet of parchment paper over it and roll out into a rough 12 1/2 x 8 1/2-inch rectangle about 1/4-inch thick. Slide the dough, still between parchment, onto a baking sheet. Repeat rolling out the chocolate dough and slide on top of the mint dough. Refrigerate for at least 30 minutes.
8. Remove the baking sheet from the refrigerator and remove the top sheets of parchment from both doughs. Flip the mint dough over onto the chocolate dough. Position so a long side is closer to you. With the parchment still covering the mint dough, roll the two doughs together into a rough 13 3/4 x 9 1/2-inch rectangle. Uncover and trim the edges to form a 12x9-inch rectangle.
9. Beginning with the long side closest to you, tightly roll up the dough into a log, using the bottom piece of parchment paper to help you. If you get to the end of the log and notice some of the pink filling poking out of the seam, use your fingers to press a little of the chocolate dough over the pink to cover. Keep the log covered in parchment paper and refrigerate for 2 hours, rolling it along the counter every 30 minutes to help maintain its round shape.
10. Arrange 2 racks to divide the oven into thirds and heat the oven to 350ºF.
11. Line 2 baking sheets with parchment paper. Unwrap the dough log and trim the ends of the log. Cut off 18 (1/4-inch thick) slices. Rewrap the remaining dough and return to the refrigerator. Transfer the slices to the baking sheets, spacing them evenly apart.
12. Bake for 6 minutes. Rotate the baking sheets between racks and from front to back, and bake until the cookies are dry and set, about 5 minutes more. Let cool for 5 minutes on the baking sheets, then transfer to wire racks and let cool completely. Repeat baking the remaining dough on cooled baking sheets (you can reuse the parchment).