Preheat oven to 375 degree F. For cookie dough, in a bowl beat shortening and the 1/3 cup butter with electric mixer on medium to high speed 30 seconds. Add brown sugar, baking soda, cinnamon, and baking powder. Beat until combined, scraping bowl. Beat in molasses, ginger, egg, and vanilla until combined. Beat in as much of the 2-3/4 cups flour as you can with the mixer. By hand, stir in remaining flour. Divide the dough in half. Cover and chill for 3 hours or until easy to handle.
Meanwhile, for Decorating Dough, in a medium bowl beat the 10 tablespoons butter with electric mixer on medium to high speed 30 seconds. Gradually add the 1 cup flour and the corn syrup, beating on low to medium speed until smooth. Mixture should be the consistency of thick frosting. Divide and tint with food coloring paste. (For these cookies we tinted 1/3 cup red, 1/3 cup purple, and 1/3 cup yellow.) Place Decorating Dough in decorating bags fitted with #6 tip.
On a lightly floured surface, roll half the cookie dough at a time to 1/8-inch thick. Using a 6-inch mitten cutter or cardboard pattern, cut cookies. If desired, use a bamboo skewer to press designs into dough. With a large spatula (or 2 small spatulas) carefully transfer cookie to an ungreased cookie sheet. Decorate with colored Decorating Dough. Bake 10 to 12 minutes or until edges are lightly browned. Cool on cookie sheet for 2 minutes. Carefully transfer to wire racks. Makes 12 cookies.