In a large bowl, mix together the flour and sugar. Set aside.
In a saucepan, melt the butter, shortening, coffee, and cocoa. Bring to a boil and boil 1 minute.
Stir boiling mixture into flour and sugar.
Add to it the buttermilk, eggs, baking soda, and vanilla. Mix all of this together well.
Pour batter into a greased jelly roll pan (17-1/2 by 11 inch).
Bake at 400 degrees for 20 minutes or until toothpick comes out clean.
Using the same saucepan and mixing bowl you used earlier - Melt together the butter, cocoa, milk. Pour into the bowl and stir in powdered sugar and vanilla. Stir until "lumpy's" are mostly gone!
Pour over warm brownies and spread evenly. Cool before serving.
Enjoy!