For the cookies: Using a stand mixer, cream the shortening, granulated sugar, orange peel and vanilla thoroughly, about 2 minutes. Add in the egg and beat until light and fluffy, about 1 more minute. Add in the milk and mix.
Sift the flour, baking powder and salt together, and then blend into the cream mixture. Divide the dough in half (thirds if you double your recipe), slightly flatten between 2 sheets of waxed paper and refrigerate for 1 hour (or freeze for 20 minutes).
Roll out the dough 1/4-inch thick on a lightly floured surface and cut into shapes with a cookie cutter. Transfer the shapes to lightly greased cookie sheets and chill until firm, about 30 minutes.
For the egg yolk glaze: Preheat the oven to 375 degrees F. While the dough is chilling, combine the egg yolk, 1 teaspoon water and food coloring. Paint the cookies (with a soft brush) with the egg yolk glaze.
Bake the cookies for 6 to 7 minutes. Do not allow the cookies to brown. The cookies will be slightly puffed and the glaze will look crackled. Bake in 2 batches if you don't reroll the scraps.
For the decorative white icing: While the cookies are baking, mix the powdered sugar, milk and egg whites. Make sure that it is thick and somewhat retains its shape.
Remove the cookies from the oven to a wire rack to cool completely, about 30 minutes.
Then, using a pastry bag or zip-top bag, pipe the cookies with the white icing to decorate.