Combine the butter, granulated sugar, powdered sugar and salt in the bowl of a stand mixer fitted with the paddle attachment. Mix on medium-high speed until fluffy and light in color, about 3 minutes, scraping down the sides of the bowl as necessary.

Add the egg yolks and vanilla extract. Continue to mix until thoroughly incorporated.

Reduce the mixer speed to low and add the flour. Mix until the dough just comes together.

Remove half of the dough and transfer it to a separate bowl. Set aside.

Add the cocoa powder to the half of the dough remaining in the mixer bowl. Mix on low speed until fully incorporated and no streaks of vanilla remain.

On a clean work surface or a piece of parchment paper, shape each half of the dough into a rectangle that is 9 inches long, 2 inches wide and 1 inch tall (I use my hands, a rolling pin and a dough scraper to help me create evenly-shaped rectangles). Stack the halves on top of each other, carefully wrap the whole log in plastic wrap and chill in the refrigerator for at least 3 hours or up to 2 days.

Preheat the oven to 325 degrees, move the baking racks to the lower third and upper third positions and line two baking sheets with parchment paper.

Remove the dough from the refrigerator and slice in half lengthwise. Flip one of the long strips of dough around so that the vanilla and chocolate doughs alternate in a checkerboard pattern. Press together lightly to help the dough stick together.

Slice the dough log into ¼ inch slices. Place each slice on the prepared baking sheets, leaving about an inch of space between each cookie.

Bake for 15-18 minutes, or until the cookies are just about to start turning brown on the edges, rotating the pans halfway through.

Cool slightly on the pan and then use a metal spatula to transfer to a metal cooling rack to cool completely.