Preheat oven to 325F; mist a large baking sheet with cooking spray. In a large bowl, combine both flours, baking powder, cinnamon and ginger.
Add 1/3 cup water, molasses and oil and stir until fully mixed. Knead briefly to gather dough into a ball.
Roll dough out on a lightly floured surface into a 10-inch square. If making shaped cookies, cut out with a cookie cutter and place on baking sheet, at least 1/2 inch apart. If making squares, transfer dough to baking sheet and cut into 1-inch squares with a pizza cutter.
Bake for 25 minutes, or until crisp and dry. Allow cookies to cool on baking sheet on a wire rack, then break them apart at cut lines, if necessary.
