Divide the dough in half into two equal portions. Add the cooled melted chocolate to one of the portions, then mix well until the dough is a uniform light brown color.
Shape each of the doughs into square logs, about 2” by 2” by 10”. Wrap each tightly in plastic wrap and chill in the refrigerator for at least 4 hours or overnight.
Slice each of the dough logs into 3 even slices. Lay the slices cut side down and slice each into 3 additional slices. You should have 9 strips of chocolate and 9 strips of vanilla.
Roll the reserved dough between two sheets of parchment paper until it will wrap around the cookies, then tightly wrap one checkerboard log with chocolate and the other with vanilla, using the parchment paper to help guide the rolled dough onto the logs
Tightly wrap each checkerboard dough log with plastic wrap, then return to the fridge to chill up for an additional 30 minutes-1 hour. Preheat the oven to 350°F/175°C, line a baking sheet with parchment paper, and set aside.
Slice the cookies into ¼” slices, and place cut side down on the prepared baking sheet. Bake for 8-10 minutes, or until slightly puffed and lightly golden.