In a medium bowl, add matcha powder to flour. Stir to mix well. Repeat steps above to form match dough.
When dough is chilled, remove plastic, roll on a lightly floured surface to form two 7 inch squares. Cut each square into nine ¾ inch strips.
On a sheet of plastic, place three strips of dough, alternating white and matcha strips. Brush tops and in between strips with egg wash. Gently press strips together.
Form second and third layers with alternating strips to create a checkerboard.
Wrap with plastic and refrigerate for another 30 minutes. Repeat for second log.
Preheat oven to 350˚F (180˚C).
Cut each log into ¼ inch thick slices. Place onto non-stick baking sheet. Bake for about 12 minutes.
Remove and let cookies cool for 5 minutes before transferring onto a wire rack to cool completely.