In a large mixing bowl, stir together flour, ginger, baking soda, cinnamon, and salt; set aside.
In another large mixing bowl, beat shortening and sugar with an electric mixer until well combined. Add egg, molasses, and vinegar; beat well.
Add flour mixture; beat until combined. Stir in any remaining flour by hand. Divide dough in half; wrap in plastic. Chill 3 hours or until easy to roll.
On a lightly floured surface, roll one portion of the dough at a time to 1/8-inch thickness. Using cookie cutters, cut into desired shapes. Place 1 inch apart on greased cookie sheets.
Bake in a 375 degree F oven 5 to 6 minutes or until edges are just firm. Remove from oven. Cool on cookie sheet 1 minute; transfer cookies to a wire rack and let cool. Pipe on decorator icing, if you like. Makes 72 three-inch cookies.
