Lightly grease a 12- or 13-inch pizza pan or a 13x9x2-inch baking pan; set aside.
In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, ginger, baking soda, and cinnamon. Beat until combined, scraping sides of bowl occasionally. Beat in egg and molasses until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.
Spread the dough evenly into the prepared pan.
Bake in a 350 degree F oven for 12 minutes. Sprinkle partially baked cookie with gumdrops. Return to the oven. Bake about 8 minutes more or until edges are browned (do not overbake). Cool completely in pan on a wire rack.
In a heavy small saucepan melt white baking pieces and shortening over low heat. Drizzle over cookie. Let stand about 20 to 30 minutes or until set. To serve, cut into wedges or bars. Makes 16 wedges.