Divide the dough in half, into two equal portions.
Make the chocolate dough by placing half the dough back into the mixing bowl and adding in the unsweetened cocoa powder, mixing it into the dough until combined. Set the dough aside. 3 TBS unsweetened cocoa powder
Add the extra flour to the vanilla base and work it into the dough until combined completely. 2 TBS all purpose flour
Form each of the doughs into separate rectangular blocks that are about 2x2 inch square by 6 inches long.
Wrap them each with plastic wrap and place them in the fridge for 1 hour.
Using a sharp knife, carefully cut each block into 3 even strips. Then cut each strip into thirds again to give you 9 thin strips of each dough block.
Trim off any rounded edges to try and keep the checkerboard pattern neat.
Take one vanilla strip, then a chocolate strip, then another vanilla strip and press those together. Then on top of those alternate, chocolate, then vanilla, then chocolate. Then a third row the same as the first.
Press the strips together to remove any possible gaps, and smooth out the cookie dough into smooth lines.
Repeat making a second block with the opposite colors, starting with chocolate.
Cover the logs with plastic wrap and chill for at least another hour.
Preheat the oven to 350 degrees Fahrenheit, and line a baking sheet with parchment paper.
Take one log at a time and slice the dough into 3/8 inch thick pieces. Tim the cookie edges if desired, or needed to make neat square cookies. Place the cookies onto the prepared baking sheet 2 inches apart.
For a soft cookie, bake the cookies for about 8 to 10 minutes, or until the tops are set and the edges are lightly golden. For a crunchier cookie bake about 2 to 3 minutes longer.
Let the cookies cool for about 5 minutes on the baking pan, then transfer to a wire rack to cool completely.
Bake additional cookies as needed.