Preheat oven to 350 degrees. Grease an 8 x 8 or 9 x 9 pan, set aside. In a large bowl combine flour, brown sugar, instant coffee, cocoa powder, baking powder and salt. Stir in milk, butter and vanilla. Mix until combined, do not overmix.
Pour the batter into the prepared pan and set aside.
In a small bowl combine brown sugar and cocoa powder. Sprinkle evenly over the batter.
Pour the hot water on top. Do not stir. Bake 35 to 40 minutes or until center is almost set. Allow the cake to cool for 10-15 minutes.