Preheat oven to 400F
In a large mixing bowl, combine the flour and the sugar.
In heavy saucepan, combine butter, shortening, coffee or water and cocoa. Stir and heat to boiling.
Pour boiling mixture over the flour and sugar in the bowl. Add the buttermilk, eggs, baking soda and vanilla.
Mix well, using a wooden spoon or high speed mixer.
Pour into a well buttered 17 1/2 -by- 11 inch jelly roll pan.
Bake at 400 degrees F for 20 minutes or until brownies test done in the center.
While brownies bake, prepare the frosting. In a saucepan, combine the butter cocoa and milk. Heat to boiling, stirring.
Mix in the powdered sugar and vanilla until frosting is smooth.
Pour warm frosting over brownies as soon as you take them out of the oven. Cool. Cut into 48 bars.