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TO MAKE BLACK AND WHITE DOUGH: Place butter, vanilla, sugar, and flour in the bowl of an electric mixer fitted with the paddle attachment.
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Mix on medium speed till well-combined.
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Transfer to a work surface.
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Divide the dough in half.
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Return one half to the mixer, and add in cocoa pwdr.
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Mix till well-combined.
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Wrap dough in plastic, and store, refrigerated, till ready to use.
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TO ASSEMBLE THE COOKIES: Place 20 ounces black dough between two 12- by 14-inch pcs of parchment.
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Roll out to a 7- by 12-inch rectangle, about 1/3-inch thick.
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Repeat with 20 ounces white dough.
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Refrigerateboth rectangles at least 30 min.
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Place 12 ounces black dough between two 12- by 14-inch pcs of parchment.
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Roll out to a 4 3/4- by 12-inch rectangle.
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Repeat with 12 ounces white dough.
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Refrigerateat least 15 min.
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Place 6 ounces black dough on a clean work surface.
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Roll into a 12-inch-long log, about 3/4 inch in diameter.
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Repeat with 6 ounces white dough.
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Wrap in parchment.
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Refrigerateat least 15 min.
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Remove top piece of parchment from the smaller black rectangle.
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Unwrap white log, and place lengthwise on black rectangle.
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Using bottom piece of parchment for support, wrap black dough around the white log, pressing with fingers to seal seam.
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Roll log back and forth to smooth seam.
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Repeat step with the black log and the smaller rectangle of white dough.
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Remove the top piece of parchment from the larger white rectangle.
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Place white log wrapped in black dough lengthwise on the white rectangle.
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Using bottom piece of parchment for support, wrap white dough around log, pressing with fingers to seal seam.
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Roll log back and forth to smooth seam.
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Repeat step with the black log wrapped in white dough and the larger rectangle of black dough.
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Wrap both logs in parchment.
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Refrigerate1 hour.
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Heat oven to 375 degrees.
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Line two baking sheets with parchment.
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Remove parchment from logs, and cut into 1/4-inch-thick rounds; place on sheets, spaced 2 inches apart.
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Bake cookies till barely golden brown, about 15 min.
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Transfer cookies to a wire rack to cold.
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Bake or possibly freeze remaining dough.
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Store in an airtight container up to 2 weeks.
