Beat shortening in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, brown sugar, ginger, baking soda, cinnamon, and nutmeg; beat until combined, scraping sides of bowl occasionally. Beat in egg, molasses, and 2 tablespoons rum or milk until combined. Beat in as much of the flour as you can with the mixer. Stir in remaining flour with a wooden spoon. Divide dough in half. Cover and chill at least 3 hour or until easy to handle.
Roll each half of dough on a lightly floured surface until 1/4 inch thick. Cut with a 2- or 2-1/2-inch round cookie cutter. Place cutouts 2 inches apart on a greased cookie sheet.
Bake in a 350 degree F oven for 7 to 9 minutes or until bottoms are lightly browned. Cool for 1 minute on cookie sheet. Transfer to wire racks and cool.
Meanwhile, for the rum icing, stir together sifted powdered sugar, 1 tablespoon rum, and enough milk to make of drizzling consistency.
Dip each cookie in icing and sprinkle with nonpareils, if desired. Makes about 48 cutouts.