How to Make It
In a medium bowl, whisk the flour with the baking soda, ginger, cinnamon, allspice, cloves and salt. In a large bowl, using a handheld electric mixer, beat the butter with the shortening and brown sugar at medium speed until light and fluffy, about 2 minutes. Add the molasses and egg to the butter mixture and beat until smooth. At low speed, beat in the dry ingredients until combined. Scrape the dough onto a large sheet of plastic wrap and pat it into a disk. Refrigerate until very cold and firm, at least 4 hours.
Preheat the oven to 350°. Position the racks in the upper and lower thirds of the oven. Cut the dough in half; work with one piece at a time and keep the other refrigerated. On a lightly floured surface, roll out the dough 3/8 inch thick. Flour 3-inch cookie cutters to discourage the dough from sticking. Stamp out cookies as close together as possible and transfer them to baking sheets. Gather the scraps, pat them into a disk and refrigerate until firm. Bake the cookies for about 16 minutes, or until the edges are lightly browned; shift the pans from front to back and top to bottom halfway through baking. Let the cookies cool on the sheets for 10 minutes, then transfer them to wire racks to cool. Repeat with the remaining dough and scraps.
In a large bowl, whisk the confectioners' sugar with the egg whites until moistened. Add the water and whisk until smooth. Decorate the cooled cookies with the icing, using a pastry bag with a small plain tip or using an offset spatula.