In the bowl of an electric mixer, using the paddle attachment, thoroughly mix shortening with brown sugar, egg, and molasses until smooth and lighter brown in color.
In a separate large bowl, sift together the flour, baking soda, salt, cinnamon, and ginger.
Gradually add the dry ingredients to the shortening mixture. Mix thoroughly until a smooth, stiff dough forms.
Wrap the dough securely in plastic wrap, and chill in the refrigerator for at least two hours.
Preheat oven to 375˚.
Sprinkle flour onto a cutting board or a clean counter, and roll out the chilled dough to 1/4-inch thick with a rolling pin. Cut into shapes with a knife or cookie cutters, or for round cookies you can use the mouth of a glass. (For crisper cookies, roll the dough to 1/8-inch thick.)
Carefully lift the cookies from the counter with a pancake turner or other wide flat utensil, and place 1 inch apart on a lightly greased baking sheet. You can also use a Silpat or other silicone baking mat, and skip the greasing step.
Bake for 9-10 minutes (7-8 minutes for 1/8-inch thick cookies), or until no imprint remains when lightly touched. Remove the cookies from the oven, let cool on a baking sheet for about 3 minutes, and then carefully transfer them to a wire cooling rack to finish cooling.
When cool, frost and decorate as desired.