For the vanilla sablé dough, beat butter with sugar and salt until very light, about 5 minutes on medium speed. Beat in yolk and vanilla extract.

Remove it from mixer: sift over and stir in flour.

Divide though in half and shape each into an 8-inch long cylinder, forming it in a sheet of parchment paper. Chill until firm.

For the chocolate sablé dough, beat butter with sugar and salt until very light, about 5 minutes on medium speed. Beat in egg beating until smooth. Mix baking soda with milk and add to creamed mixture.

Remove from mixer and sift over and stir in flour and cocoa.

Divide dough in half and shape each into an 8-inch long cylinder, forming it in a sheet of parchment paper. Chill until firm.

Take a cylinder of each sablé and slice in 8 equal discs. Roll discs into cylinders using slightly wet hands. Assemble checkerboard log using the beaten reserved egg white or water.

Continue to form 4x4, 2x2, or 1x2 logs. Compress slightly. Wrap in the parchment paper and chill for several hours. Repeat with the remaining two logs, or keep them tightly wrapped in the freezer to assemble another time.

Preheat oven to 325F. Slice 1/4-inch thick cookies and place on a cookie sheet lined with parchment paper.

The cookie sheet would look like this, depending on whether they are made 4x4, 2x2, or 1x2.

Bake from 15 to 18 minutes.