Add the sugar and cold butter to the bowl of a stand mixer. Mix on low until the butter starts to break down then increase the speed and mix for 4-5 minutes until it is fluffier and fully combined.
Add the egg yolks and vanilla and mix until combined. Add the flour and salt and mix again. The dough will be very shaggy but do no fear! With the mixer on low, slowly add the cold water until the dough comes together.
Divide the dough in half. Add one half back to the stand mixer. Add the cocoa powder (or ube powder) and mix until just combined. Wrap each half in plastic wrap and chill in the fridge for at least an hour, or overnight.
Preheat the oven to 350F then remove the chilled dough from the fridge. Carefully roll out each dough ball into a rectangle that is 1/4” thick and about 6x8". The dough will be very cold. Be patient and the dough will start to work with you. Try to make the two dough balls as similar in shape as you can. Once both dough balls are rolled out, stack them on top of each other, gently pressing down to adhere the two pieces together. Cut the stacked rectangle in half, then stack one half on top of the other, making sure the colors are alternating. Transfer the dough to the fridge for 10 minutes to chill.
Remove the dough from the fridge and use a sharp knife to cut the dough into slices that are 1/4" thick. Once the dough is cut bring one slice in front of you. Grab another slice and stack it on top, making sure the colors are alternating (if the vanilla dough is on the left, the piece going on top should have the chocolate dough on the left). Gently press down to adhere the two pieces together. Repeat with two more pieces, so you have 4 total pieces stacked, making sure the colors are alternating with each piece. Cut off the rough ends from each end, revealing a checkerboard pattern.
Sprinkle each side of the stacked dough with turbinado sugar (optional). Slice the rectangular log of dough into 1/4" thick slices. Transfer up to 12 cookies onto a parchment paper lined baking sheet. Transfer the cookies to the oven and bake for 7-9 minutes, until the cookies barely don't look doughy. Repeat with the remaining dough (you should have about 3 rectangular logs of dough, each making about 12 cookies).
Let the cookies rest on the baking sheet for 5 minutes then transfer to a cooling rack to cool completely. Keep any leftover cookies in an airtight container. Enjoy!!