Preheat the oven to 350 degrees.
In a large bowl mix together the sugar and flour for the cake.
In a medium saucepan mix 1 stick of butter, cocoa, shortening and water.
Bring to a light boil.
Pour over the flour mixture and mix until blended with an electric mixer.
Add buttermilk, eggs, vanilla and soda; mix until blended.
Pour into a greased 11x17 inch pan.
Bake for 20 minutes.
While the cake is baking make your icing.
In a large bowl add the melted butter, milk and cocoa; stir until blended.
Add the vanilla and powdered sugar.
Beat until well blended.
Let the cake sit for 5-10 minutes before pouring icing over.