Whisk together the flour, pudding mix, baking powder and salt. Set aside.
In a mixing bowl, using an electric mixer, beat the softened butter and sugar until creamy. Add the eggs, one at a time, beating and scraping sides of bowl, then beat in the vanilla extract.
Add the flour mixture and stir by hand to form a very soft yellow dough. Cover bowl and chill for about 30 minutes.
Scrape dough onto a sheet of plastic wrap and shape into a log. Wrap log and chill for an hour or until firm.
To form the cookies you have a couple of options. You can cut ½ inch rounds or you can flatten out the dough and punch 2 ½ inch rounds. This really depends on how good you are at making perfectly round logs.
After forming about 20 rounds, arrange them 2 ½ inches apart on parchment lined baking sheets. Bake one sheet at a time at 325 degrees F. for about 15 minutes or until edges just start to brown.
Allow cookies to cool for 5 minutes on sheets, then transfer to a wire rack and let cool completely.
To make the chocolate frosting, heat the 3 tablespoons of cream with the corn syrup just until it starts to boil. I did this in the microwave and it took about 30 seconds. You can also use a saucepan. Combine with the chopped chocolate and stir until mixture is smooth. Let cool slightly and then carefully spread over half of each cookie. Allow the black to set while you prepare the white frosting. I recommend putting the cookies in the refrigerator to set it quickly. It makes things less messy when adding the white.
To make the white frosting, mix together the softened butter and sugar, then add 1 tablespoon of the milk. Beat until blended and keep adding milk until the icing is smooth and thin enough to spread. Beat in vanilla and salt. Pipe or just carefully spread icing on other half of cookies. You''ll probably have some left.
If you have some freezer space, put the cookies in a container with a lid that won't touch the frosting, then let them freeze. When frozen, transfer to a freezer bag and store in the freezer. Allow the cookies to come to room temperature before serving.
Notes
The measurements from the magazine are 1 ½ cups of flour and 6 ⅜ oz. This is a pretty light measurement for 1 ½ cups of all-purpose flour but pretty much exactly the weight of 1 ½ cups of cake flour. If you are using all-purpose, I recommend weighing the flour. If you don't have a scale, stir the flour well and measure with a very light hand.