Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13 inch pan.
In a large bowl, stir together the flour, sugar, baking soda and 1/3 cup cocoa. In a small saucepan, combine water and 2/3 cup of butter; bring to a boil. Allow the butter and water to cool down a bit before adding to the dry ingredients. Beat in the buttermilk and eggs last. Spread evenly into the prepared pan.
Bake for 30 to 35 minutes in the preheated oven. Allow to cool for 20 minutes before frosting.
To make the frosting: In a large bowl, stir together the confectioners' sugar, 1/3 cup cocoa, milk and vanilla until smooth. Beat in the melted butter until light and fluffy. Spread over brownies while they are still slightly warm. Cut into squares when cool.