Preheat the oven to 400° F. Cut parchment paper to cover a large baking sheet. If making large cookies, trace four 4½-inch circles on each sheet of parchment. If making smaller cookies, trace four 3½-inch circles. Place oven rack in the center of the oven.

In a large bowl, using a hand-held or stand mixer, cream together the sugar, shortening, and butter until light and fluffy.

Reduce speed to medium and add the corn syrup, then the eggs, one at a time, beating after each until just incorporated.

In another large bowl, combine the flours, baking powder, and salt.

On medium speed, beat the dry ingredient mixture into the creamed mixture, alternating with milk, and beginning and ending with dry ingredients. Add vanilla, lemon, and orange flavorings.

To make large cookies, place ½ cup batter in the center of each circle and spread evenly with the back of a spoon or rubber spatula to fill the outline. Bake one tray at a time for 10 minutes, or until the bottoms are golden.

To make smaller cookies, spread ¾ cup batter in each circle. Bake one tray at a time, for 8 minutes, or until the bottoms are golden.

To make the vanilla icing, combine the ingredients in the top of a double boiler over barely simmering water. Stir until well combined. The mixture will be thick. Cook to 100 degrees. If too thick, add a few drops of water. Remove from heat; keep icing over hot water.

Turn cookies over and frost one half of the flat side with vanilla icing. You can use a piece of wax paper as a guide for an even line of icing. Using a pastry brush (or paintbrush) instead of a spatula or knife gives the smoothest surface. To keep icing glossy, don’t go over it too much. Place on a rack to dry.

To make chocolate icing, add melted chocolate to vanilla icing. Apply the chocolate icing when the vanilla icing dries.