In a medium bowl, whisk the flour and salt together. Set aside.
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter with the sugar. Add the vanilla extract and beat to incorporate. Add the dry ingredients and mix on low speed until combined. Divide the dough, leaving half in the mixing bowl. Add the cocoa powder and beat until combined.
Use your hands to form each half of dough into a rectangle log, measuring about 6 inches long and 2 inches wide. Make sure both logs are the same size. Wrap each one tightly in plastic wrap and chill in the refrigerator for one hour.
Remove the dough from the refrigerator. Slice each log into 3 even-sized strips. Flip each strip once onto its side and slice into 3 more thin strips, so that you have 9 strips from each log.
Place 3 alternating strips of dough side-by-side, using your hands to gently press them together. Proceed to stack the remaining strips on top, creating a checkerboard pattern with alternating strips, until all of the cookie dough has been used up. Wrap tightly in plastic wrap and chill in the refrigerator for another 30 minutes.
Preheat the oven to 350°F. Line baking sheets with parchment paper and set aside.
Remove the cookie dough from the refrigerator. Slice into individual cookies, about ¼ inch thick, and arrange on prepared baking sheets. Bake for 10-12 minutes. Allow the cookies to cool on the baking sheets completely before removing. The cookies will be soft.
If the cookie dough starts to break apart as you are cutting the strips or assembling the checkerboard pattern, simply use your hands to press it back together. It should stick together very easily.
I wanted to make big cookies, so I stacked all of the strips together to form larger cookies. If you'd like, you can form two stacked logs, using up 9 strips total for each. This will give you smaller cookies.