In a medium bowl combine the flour, sugar, baking powder, salt, and 2 tablespoons of cocoa powder. Stir in the milk and vanilla.
Spread the batter evenly in an ungreased 9-inch square pan.
Combine the remaining 4 tablespoons of cocoa powder with the brown sugar and hot water. Carefully pour the mixture over the batter. DO NOT stir the mixture into the batter.
Bake for 35 to 40 minutes. Serve warm with ice cream, if desired.