Stir together 3/4 cup sugar, flour, 3 tablespoons cocoa, baking powder, and salt. Stir in milk, butter, and vanilla, mixing until smooth. Pour into an ungreased 8-inch square glass baking pan.
In a small bowl, mix 1/2 cup sugar, brown sugar, and 4 tablespoons cocoa. Sprinkle evenly over batter. Pour hot water over the top. Do not stir.
Bake for 35-40 minutes, or until center is almost set. Let stand for 15 minutes, then serve. Use the chocolate sauce in the bottom of the pan to spoon over servings. Garnish, if desired, with ice cream or whipped cream.