In a large mixing bowl, cream together granulated sugar and vegetable shortening. Add the vanilla extract, eggs and egg yolks, one at a time. Combine well. Scrape the bowl with a rubber spatula occasionally. Sift together the flour, salt and baking powder.
Add the sifted flour and milk, alternating between the two. Mix for about 1 minute, scrape the bottom and sides of the bowl, making sure everything is thoroughly combined. Line regular size cupcake pan with papers. Scoop evenly into 18 cupcake papers.
Bake in a preheated 350 degree F oven for about 22-24 minutes or until a toothpick when inserted comes out clean. Let cupcakes cool completely.
In a large bowl, using a hand mixer on slow speed, beat together powdered sugar, salt, unsweetened cocoa powder, softened butter and whole milk. Add a little more milk if needed. Whip on high speed until the frosting is smooth and the consistency you desire.
Scoop the frosting into a pastry bag or a large zip-style bag, cut the tip off and pipe evenly onto the cupcakes.