Preheat the oven to 350 degrees F (175 degrees C).

Sift flour, 3/4 cup white sugar, baking powder, and salt together in a bowl. Mix in milk, butter, vanilla extract, and chocolate. Pour mixture into an ungreased 8x8-inch baking pan.

Mix brown sugar, cocoa, and remaining white sugar together in another bowl. Spread over the top of the batter in the pan. Pour in water.

Bake in the preheated oven until a toothpick inserted into the center comes out mostly clean, about 30 minutes. Allow to cool in the pan for 15 to 30 minutes. Serve warm.