Preheat oven to 400 degrees.

In a large mixing bowl, combine the flour and 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 electric mixer.

Pour into a well-buttered 17 1/2" x 11" jelly roll pan.

Bake 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.