Beat shortening in a mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, ginger, baking soda, cinnamon, and cloves. Beat until combined. Beat in molasses, egg, and vinegar 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 about 3 hours or until easy to handle.
Roll each portion of dough on a lightly floured surface until 1/8 inch thick. Cut with a floured Indian shape cutter.
Bake in a 375 degree F oven for 5 to 6 minutes or until edges are lightly browned. Cool 1 minute on cookie sheet. Transfer to wire racks to cool. Makes 24 to 30 cookies.