Melt the butter. Add the sugars and cocoa and blend well. Beat eggs in, one at a time. Combine flour and baking powder and stir into mixture. Add the vanilla and nuts. Pour into a greased 13- by 9-inch pan. Bake for 30 minutes. Ice when cool.
Place first 3 ingredients in a food processor and, using steel knife, blend for 4 seconds. Add remaining liquids and blend until smooth. Add additional milk, if necessary.