In the bowl of an electric mixer fitted with the flat beater paddle, beat together the butter, sugar and vanilla on medium speed until light and fluffy, about 2 minutes.

Sift the flour. Add half of the flour to the butter mixture and beat on medium-low speed until just combined. Add the egg and the remaining flour and beat until completely combined, 1 to 2 minutes.

Transfer the dough to a sheet of parchment paper and divide in half. Place 1 piece of dough in a medium bowl and add the cocoa. Using a silicone spatula or your hands, fold until completely combined. Make sure the dough takes on the dark color of the cocoa with no visible streaks of plain dough.

Divide each piece of dough (plain and chocolate) in half so you have 2 pieces of plain dough and 2 pieces of chocolate dough. On another sheet of parchment paper, using your hands, roll each piece of dough into a cylinder about 12 inches long.

Keeping the dough on the parchment, arrange the cylinders to form a checkerboard pattern: Place 1 chocolate cylinder next to a plain cylinder and lightly press them together. Then layer the top, reversing the order of the 2 cylinders. Wrap the log of dough with parchment paper along its length. Smooth the edges and gently press the cylinders together using the outer parchment paper to create a cleaner finish, more squared off finish. Refrigerate until the dough is firm, about 1 hour.

Preheat an oven to 350°F. Line 2 baking sheets with parchment paper.

Remove the dough from the refrigerator and unwrap it. Using a sharp knife, cut the dough crosswise into slices about 1/4 inch thick. Place on the prepared baking sheets, spacing the cookies about 1-2 inches apart. Refrigerate the cookies on baking sheets until firm, about 10 minutes.

Bake until the cookies are just turning golden brown at the edges, 10 to 15 minutes. Transfer the baking sheets to wire racks and let cool for 5 minutes, then transfer the cookies to the racks and let cool completely. Store in an airtight container at room temperature. Makes about 55 cookies.