Preparation

• 1 In a food processor, combine the flour, sugar and salt. Add the butter pieces in 2 additions, pulsing after each addition, until the mixture resembles coarse crumbs.
• 2 Add the egg yolk and vanilla and pulse until the dough holds together. Divide the dough in half. Transfer one-half to a lightly floured work surface and knead in the cocoa until incorporated.
• 3 Lightly dust the work surface and a rolling pin with flour. Roll out each dough half into a 3-by-9-inch rectangle, 1/2 to 3/4 inch thick; trim the edges to even out. Place each rectangle on a large baking sheet and cover with plastic wrap.
• 4 Refrigerate until well chilled, about 30 minutes. Meanwhile, in a small bowl, beat the whole egg until blended. Set aside.
• 5 Remove the dough from the refrigerator. Using a sharp knife, cut each rectangle into 4 strips about 3/4 inch wide (you should have 4 strips of each color). Arrange 2 chocolate strips and 2 plain strips in a checkerboard pattern, brushing the beaten egg between the strips and gently pressing them together. Repeat with the remaining dough. Wrap in plastic wrap and use a knife to square off the edges of each block. Refrigerate until well chilled, about 30 minutes.
• 6 Preheat an oven to 350°F. Lightly grease 2 baking sheets or line them with parchment paper.
• 7 Remove the blocks from the refrigerator, unwrap and cut each crosswise into slices 1/4 inch thick. Place them 1 1/2 inches apart on the prepared baking sheets. Bake until the cookies feel firm when lightly pressed, about 15 minutes. Let the cookies sit on the baking sheets for 2 minutes, then use a spatula to transfer them to wire racks to cool completely. Makes about 5 dozen cookies.