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1
In a food processor, combine the flour, sugar and salt.
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2
Add the butter pieces in 2 additions, pulsing after each addition, until the mixture resembles coarse crumbs.
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3
Add the egg yolk and vanilla and pulse until the dough holds together.
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4
Divide the dough in half. Transfer one-half to a lightly floured work surface and knead in the cocoa until incorporated.
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5
Lightly dust the work surface and a rolling pin with flour.
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6
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.
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7
Place each rectangle on a large baking sheet and cover with plastic wrap.
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8
Refrigerate until well chilled, about 30 minutes. Meanwhile, in a small bowl, beat the whole egg until blended. Set aside.
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9
Remove the dough from the refrigerator.
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10
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.
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11
Wrap in plastic wrap and use a knife to square off the edges of each block.
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12
Refrigerate until well chilled, about 30 minutes.
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13
Lightly grease 2 baking sheets or line them with parchment paper.
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14
Remove the blocks from the refrigerator, unwrap and cut each crosswise into slices 1/4 inch thick.
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15
Place them 1 1/2 inches apart on the prepared baking sheets.
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16
Bake until the cookies feel firm when lightly pressed, about 15 minutes.
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17
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.
