In a large bowl, mix together flours, baking soda, baking powder, salt, and spices. Using an electric mixer, cream butter until soft, then add brown sugar and beat until well-mixed. Add molasses and beat, scrape down and add egg, beat again until combined. Stir in the flour mixture. Divide dough into four rectangular pieces, place between sheets of parchment and roll out ¼” thick. Stack sheets of dough on a baking pan and chill for 3 hours.
Preheat oven to 350ºF. Lay sheets of dough on counter, remove top layer of parchment and use a cookie cutter to cut into shapes. Using a thin spatula, transfer cookies to parchment-lined baking sheets. Repeat with scraps. Bake 12 minutes, switching the pans between oven racks halfway through. When cookies are puffed and look dry, remove and cool on the pan for five minutes, then move cookies to a cooling rack.
Using an electric mixer, mix powdered sugar with egg white. Mix in lemon juice and water, a tablespoon at a time, to reach desired consistency. Transfer icing to a piping bag with a small round tip and use to draw outlines on the cookies.