In a large mixing bowl, measure flour and sugar. Set aside.
In a medium sauce pan, combine butter, water, cocoa and shortening. Bring to a boil. After mixture reaches a boil, add it to the flour mixture and stir to combine.
Add buttermilk, then baking soda, then eggs, then vanilla in that order, mixing in-between each addition.
Pour into a greased cookie sheet and bake at 400 degrees F for 20 minutes!
Frosting
Bring combine butter milk and cocoa and bring to a boil. Remove from heat and stir in powdered sugar and vanilla until smooth.
After cake has cooked, remove from oven and poke holes in hot cake with a fork. Pour frosting evenly over top.