Double your pleasure by topping this off with whipped cream or vanilla ice cream.
Preheat oven to 350 degrees F. Grease a 9-inch baking dish.
Combine flour, sugar, 2 tablespoons of cocoa powder, baking powder, and salt in a large bowl. Whisk to blend.
In a separate bowl, combine brown sugar and remaining cocoa powder. Whisk to blend.
Make a well in the center of the flour mixture. Add the egg, milk, melted butter, and vanilla and whisk until blended. Spread the batter evenly into the prepared baking dish. Sprinkle with chocolate chips, then with brown sugar mixture. Slowly pour boiling water over the batter. Put the pan on the center oven rack and bake for 30 minutes. (When done, the cake will be baked through with a layer of pudding underneath.) Cool for 20 to 30 minutes to allow pudding to thicken.