1. In a large bowl, whisk together the flour, baking powder and salt. Set aside.
2. In a separate bowl, beat together the sugar and butter until pale and fluffy. Beat in the eggs, egg whites and vanilla extract until well combined.
3. Add the flour mixture to the sugar mixture and stir just until the dough comes together.
4. Turn out the dough onto a clean work surface and form it into a ball. Divide the dough in half.
5. Sprinkle cocoa powder over one of the halves of the dough. Knead the cocoa into the dough until it is fully incorporated.
6. Form dough into two square logs (about 10.5 inches/26 cm in length, and 2 inches/4.5 cm in width). Wrap well in plastic wrap and place into freezer to firm up; about 20 to 30 minutes.
7. Using a sharp chef’s knife and a ruler, slice each log lengthwise into thirds. You will end up with three chocolate and three white strips, each 10.5 inches/26 cm long.
8. With a damp pastry brush, lightly brush water onto one side (the 2 inch/4.5 cm side) of a white layer. Place a chocolate layer on top of the white layer and gently press down. Lightly brush the chocolate layer with some water and gently press down a white layer. Wrap well in plastic wrap and place into freezer to firm up. Repeat process with the remaining layers (chocolate/white/chocolate). Freeze for at least 30 minutes before slicing.
9. Take chilled logs out of the freezer. With either the white or chocolate layer facing up, slice the two logs into thirds again. You should now have 6 layers of striped dough. Place one layer of dough, the 2 inch/4.5 cm facing up, and brush lightly with water. Place another layer, making sure the colours are alternating, on top of the brushed layer and press down gently. Brush the second layer with water and place the final layer on top. Wrap the checkerboard log well in plastic wrap and place into freezer, until ready to use. Repeat process with the last 3 layers, ensuring the colours are alternating. You will have one log where the outer corners are chocolate, and the second log where the corners are white. Freeze for at least 30 minutes before baking. (The dough can be frozen for up to 2 months.)
10. When ready to bake, preheat the oven to 350°F. Line a large baking sheet with parchment paper.
11. Remove one log of dough from the freezer. Unwrap the log and, with a sharp knife, cut crosswise into half-inch slices. Place the slices, about 1/2 inch apart, on the prepared baking sheet. Bake until the cookies are lightly golden, 10 to 14 minutes. Let the cookies cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely. Repeat with the remaining logs, if liked. (The cookies can be stored in an airtight container at room temperature for up to 4 days, or frozen, with parchment paper between the layers, for up to 2 months).
