For vanilla dough, cream butter and sugar together in a large bowl until well blended, about 2 minutes. Beat in vanilla extract.
Gradually mix in flour on low speed.

Knead dough to bring it together. Turn dough onto a clean working surface. Shape into a rectangle. Wrap with plastic and chill for about 30 minutes.

For chocolate dough, cream butter and sugar together in a large bowl until well blended, about 2 minutes.
Beat in cocoa powder. Gradually mix in flour on low speed.

Prepare 4 sheets of parchment or wax paper. Draw a 7-inch x 7-inch square in the middle of 2 of the 4 sheets of parchment or wax paper.

When both types of dough are chilled, remove from refrigerator.
Place a sheet of the parchment paper with the drawn side of the 7-in x 7-in square facing down on your work surface. Unwrap dough and place in the middle of the 7-in x 7-inch square. Then place another sheet of parchment paper (not drawn) on the top of dough.

Roll out dough to the outline of the 7-in x 7-in square. Use a knife or spatula to push dough into the square so as to minimize wastage. Trim dough if necessary.
Remove the top parchment paper and cut dough into three slabs of equal width

Do the same for the other flavor of dough.

Place three slabs of dough, alternating vanilla and chocolate dough one on top of the other. Gently press the slabs together.
Cut each slab lengthwise into 3 strips of equal width.
Rearrange the strips of dough to create 2 slabs forming 9 small rectangles cross-wise.

Wrap each slab with plastic and refrigerate for another 30 minutes.
Preheat oven to 350°F (180°C).
Remove dough from refrigerator. Unwrap the dough and slice each log into ¼ inch thick slices cross-wise.

Place onto non-stick baking sheet and bake for about 12 minutes per batch.

Remove and let cookies cool for 5 minutes before transferring onto a wire rack to cool completely.