Preheat the oven to 350 degrees F.
For the cake: Whisk together the sugar, flour, cocoa, baking powder and salt in a bowl. Whisk in the milk, butter and vanilla. Stir together until smooth with a wooden spoon or spatula.
Pour the batter into an ungreased 9-inch square baking pan. Use an offset spatula to level into pan.
For the topping: Whisk together the sugars and cocoa and sprinkle it evenly over the batter. Pour the hot water over the top, resist the temptation to stir it into the batter.
Bake about 30 minutes, you want the center to bubble and look almost set, almost like an undercooked brownie. Take out of the oven and let stand 15 minutes. Serve in dessert dishes, spooning sauce from bottom of pan over top. Serve with mint chocolate chip ice cream, if desired.