Sift together flour, cocoa powder, baking soda, and salt into a medium bowl; set aside.
In the bowl of a standing mixer fitted with the paddle attachment, cream the butter and sugar until light and fluffy, about 2 minutes. Add egg white; beat to combine. With mixer on low speed, gradually add the flour mixture until combined.
Form dough into a disc and wrap in plastic. Refrigerate 45 minutes until firm.
Preheat oven to 350 degrees. Roll dough between two pieces of parchment into an 11-by-15-inch rectangle. Prick all over with a fork. Bake until set, 12 to 14 minutes.
Cool on a wire rack. Break cookie into pieces and place in a zipper lock bag. Use a rolling pin to break into coarse crumbs.