Stir together 3/4 cup (150g) sugar, flour, 3 tablespoons (16g) cocoa, baking powder, and salt. Stir in the 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 (100g) sugar, brown sugar, and 4 tablespoons (21g) cocoa powder. Sprinkle evenly over the batter. Pour the hot water over the top. Do not stir.
Bake for 35-40 minutes, or until the 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. Serve, if desired, with ice cream or sweetened whipped cream.
Notes
Store covered in the refrigerator up to a week. Reheat for serving.