In a large bowl, whisk together the flour, sugar, and salt.
In a medium saucepan, bring the stick of butter, shortening, water, and cocoa to a boil. Once boiling, remove from heat and pour over the flour mixture.
Add the eggs, baking soda, buttermilk, and vanilla to the above mixture and whisk well.
Prepare an 18x13 cookie sheet pan with bakers spray. Evenly pour and spread the batter onto the prepared pan. Bake at 350 degrees Fahrenheit for about 23 minutes, or until set on the edges and a toothpick inserted in the center comes out clean.
For the icing, bring the butter, cocoa, milk, and powdered sugar to a boil over medium heat. Whisk in the vanilla until the icing is smooth and creamy. You can do this portion with an electric mixer to aerate it a bit (I like this method).
Pour the icing over the cake. It's ideal for the cake to still be warm to the touch, but not too hot, otherwise the icing will seep in and not set well on top.