Grease 8" square pan. Heat oven at 350°.
Combine 1 cup sugar and 2 eggs; beat.
Melt 2/3 cup butter. Add to egg mixture. Whisk flour and 4 tablespoons cocoa together, blend into sugar/egg/butter mixture with 1 teaspoon vanilla and nuts. Spread in pan - bake 20-25 minutes.
Combine 1 cup sugar, 1 egg beaten, 3 tablespoons cocoa, 1/3 cup butter, 1 teaspoon vanilla, 2 tablespoons light cream.
Bring slowly to a boil; stirring constantly. Remove from heat and stir until of spreading consistency.
Cook's Note : I make the frosting in the same heavy sauce pan in which I melted the butter for the brownies. Make sure that the sugar has dissolved in the frosting before you take it off the heat. As long as the brownie has cooled; go ahead and pour the frosting on it, it'll firm up as it cools. But wait for the topping to firm up before you cut it into squares if you can resist!