Place butter, vanilla, sugar, and flour in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until well combined. Transfer to a work surface.
Divide dough in half. Return half to the mixer, and add cocoa powder. Mix until well combined. Wrap dough in plastic, and store, refrigerated, until ready to use.
Place 20 ounces of the dark-colored dough between 2 pieces of parchment paper. Roll out to a 7 by 12-inch rectangle, about 1/3-inch-thick. Repeat with 20 ounces white dough. Chill both rectangles at least 30 minutes.
Place 12 ounces of the dark-colored dough between 2 pieces of parchment paper. Roll out to a 4 3/4 by 12-inch rectangle. Repeat with 12 ounces white dough. Chill at least 15 minutes.
Place 6 ounces of the dark-colored dough on a clean work surface. Roll into a 12-inch long log, about 3/4-inch in diameter. Repeat with 6 ounces white dough. Wrap in parchment. Chill at least 15 minutes.
Remove top piece of parchment from the smaller black rectangle. Unwrap white log, and place lengthwise on black rectangle. Using bottom piece of parchment for support, wrap black dough around the white log, pressing with fingers to seal seam. Roll log back and forth to smooth seam.
Repeat above step with the black log and the smaller rectangle of white dough.
Remove the top piece of parchment from the larger white rectangle. Place white log wrapped in black dough lengthwise on the white rectangle. Using bottom piece of parchment for support, wrap white dough around log, pressing with fingers to seal them. Roll log back and forth to smooth seam.
Repeat above step with the black log wrapped in white dough and the larger rectangle of black dough. Wrap both logs in parchment. Chill for 1 hour.
Preheat oven to 375 degrees F.
Line 2 baking sheets with parchment. Remove parchment from logs, and cut into 1/4-inch thick rounds; place on prepared baking sheets, about 2 inches apart.
Bake cookies until barely golden, about 15 minutes. Transfer cookies to a wire rack to cool. Bake or freeze remaining dough. Store in an airtight container up to 2 weeks.