Spread into prepared pan (batter will be very thick and sticky) and bake for about 30 minutes, until a tester comes out mostly clean. The edges should be set and the center should still look slightly moist, but not uncooked.
To make the frosting, melt the 1/2 cup of butter and stir in the cocoa. Remove from the heat. Whisk in the powdered sugar, vanilla, and milk until smooth. Pour over the brownies and smooth with an off-set spatula.