Place butter in a 9×13-inch baking dish and put in oven. Once butter has melted, remove and set aside.
Stir together the 1 1/2 cups sugar, 4 tablespoons cocoa powder, flour, milk, baking powder, salt, and vanilla extract. Spoon into baking dish over melted butter, but do not stir.
In a separate bowl, mix together the 2 cups sugar and 1/2 cup cocoa powder. Sprinkle over batter in pan. Pour boiling water over topping, but again do not stir.
Bake until top has set, 35-40 minutes. The bottom will be loose and a bit gooey.