To make the chocolate dough, use the first set of ingredients. In a medium bowl, cream together the confectioners' sugar and butter. Stir in the egg. Combine the flour, salt and cocoa, stir into the creamed mixture alternately with the milk. Set aside.
To make the pistachio dough, use the second set of ingredients. In a medium bowl, cream together the confectioners' sugar and butter. Stir in the egg. Combine the flour and salt, stir into the creamed mixture. Finally, stir in the pistachios and food coloring.
On a lightly floured surface, pat out each dough to a rectangle 6x5 inches. Cut each rectangle crosswise into 8- 3/4 inch strips. Place 1 strip of each color side by side. Place two more strips on top of those, alternating colors. Repeat until the checkerboard is 4 strips high. Use remaining strips to form a second rectangle. Wrap rectangles and refrigerate at least 2 hours, or until firm.
Preheat oven to 375 degrees F (190 degrees C).
Unwrap the dough and slice crosswise into 1/4 inch slices. Place 1 inch apart on an ungreased cookie sheet.
Bake for 8 to 10 minutes in the preheated oven, or until set. Remove cookies from baking sheet to cool on wire racks.