Cream together the butter and sugar until light and fluffy. This will take about 3 minutes with an electric mixer on medium speed.

Beat in the egg yolks one at a time, then stir in the vanilla extract.

In a separate bowl, whisk together the flour, matcha powder, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix, as this can toughen the cookies.

Divide the dough into two equal halves. Tint one half with green food coloring.

Roll out each half of the dough on a lightly floured surface into a 12x8-inch rectangle.

Cut each rectangle into 8 (1x3-inch) strips.

Arrange the strips of dough alternately on a baking sheet lined with parchment paper, creating a checkerboard pattern.

Chill the dough for at least 30 minutes. This will help the cookies to keep their shape and bake evenly.

Preheat oven to 375 degrees F (190 degrees C).

Bake the cookies for 13-14 minutes, or until the edges are golden brown.

Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.