Cut nonstick baking parchment to fit your baking sheet. Stir together the dry ingredients in a large bowl. Combine the corn syrup, brown sugar, and margarine in a 2-quart saucepan. Stir constantly over medium heat until margarine is melted. Pour the syrup mixture over the flour mixture.
Stir well, using your hands to mix as the dough becomes stiff. If you are using a heavy-duty Kitchen Aid mixer, the mixer can handle this dough; lightweight mixers cannot. Chill the dough 1 hour or until it is about room temperature. Preheat oven to 350 degrees Fahrenheit. Roll out the dough on nonstick baking parchment to a thickness of 1/8-inch. Using the patterns of your choice, cut out the necessary pieces. Bake 12 to 15 minutes or until golden brown. Smaller pieces should be baked separately from larger ones, as baking times will vary depending on size. Check for air bubbles during baking and poke them with a knife or skewer. When baking is done, slide the parchment with the hot gingerbread onto a cooling rack. Make sure all the pieces lie flat.
For the icing: Sift the confectioners' sugar. Place the egg whites in a mixer bowl. Add sugar and cream of tartar to egg whites while stirring. When all the sugar is incorporated, turn mixer to high and beat mixture until thick and very white. The icing should hold a stiff peak. The process takes about 5 to 7 minutes, longer if using a hand mid mixer. Cover the icing tightly with plastic wrap, as it dries very quickly. Use paste food colors to tint the icing. A tiny dot on a toothpick to a quarter cup of icing will make a nice pastel color, but be sure to add it a little at a time. With practice you will learn how much to use to get the color intensity you want.