Dough
1.To make the white dough, place 2 cups (4 sticks) butter, 1/2 teaspoon vanilla, 1 1/2 cups sugar, and 3 3/4 cups flour in the bowl of an electric mixer fitted with a paddle attachment. Mix on medium speed until well combined. Wrap the dough in plastic.
2.To make the black dough, combine, in the same bowl, the remaining 2 cups (4 sticks) butter, 1/2 teaspoon vanilla, 1 1/2 cups sugar, 3 3/4 cups flour, and the cocoa powder. Mix on medium speed until well combined. Wrap the dough in plastic. Store dough in the refrigerator up to 2 weeks or freeze up to 3 months.
Cookies
1.Place 20 ounces black dough between two 12-by-14-inch pieces of parchment. 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.
2.Place 12 ounces black dough between two 12-by-14-inch pieces of parchment. Roll out to a 4 3/4-by-12-inch rectangle. Repeat with 12 ounces white dough. Chill at least 15 minutes.
3.Place 6 ounces black 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.
4.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.
5.Repeat step four with the black log and the smaller rectangle of white dough.
6.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 seam. Roll log back and forth to smooth seam.
7.Repeat step six with the black log wrapped in white dough and the larger rectangle of black dough. Wrap both logs in parchment. Chill 1 hour.
8.Heat oven to 375 degrees. Line two baking sheets with parchment. Remove parchment from logs, and cut into 1/4-inch-thick rounds; place on sheets, spaced 2 inches apart.
9.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.
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