In a large bowl, combine flour and sugar. Set aside. In heavy saucepan, combine 1/2 cup butter, shortening, water, and 1/4 cup cocoa. Stir and heat to boiling. Poor boiling mixture over flour/sugar mixture. Add the buttermilk, eggs, baking soda, and 1 tsp. vanilla. Mix well with wooden spoon. Pour into 17 1/2” x 11” jelly roll pan. Bake at 400 degrees for 15-20 minutes or until done. While brownies bake, prepare frosting. In a saucepan, combine 1/2 cup butter, 2 Tbsp. cocoa, and milk. Heat to boiling, stirring. Add the powdered sugar and 1 tsp. vanilla and stir until smooth. Let cool slightly, then pour over the slightly cooled brownies. Cool completely before cutting.