Preheat oven to 400F.
In a large bowl, whisk together flour and sugar. Set aside.
In saucepan, melt butter and shortening with coffee and cocoa, whisking to combine. Heat to a gentle boil.
Add flour mixture to the saucepan and mix to fully combine.
Add buttermilk, eggs, baking soda and rum or vanilla. Mix well to combine.
Pour into greased and lined 17” by 11” baking sheet.
Bake at 400F for 20 minutes, or until batter is just cooked through in the center *brownies will continue to bake for a few minutes once removed from oven
While the brownies are baking, prepare frosting.
In a saucepan over medium heat, combine butter, cocoa and milk. While stirring, heat to boiling.
Sift in powdered sugar, one cup at a time. Whisking well with each addition to fully combine.
Add coffee or vanilla. Whisk.
Pour the warm frosting over the pan of warm brownies right out of the oven.
Allow to set and cool. Slice and serve!