Preheat the oven to 350°F.
Place an unwrapped stick (1/2 cup) of butter in a 13×9 inch baking dish and place it in the oven to melt completely.
In a large bowl, whisk together the flour, baking powder, salt, cocoa powder, and granulated sugar.
Stir in the milk and vanilla extract until the mixture comes together. It will be very thick, almost like cookie dough.
In a separate bowl, mix together the granulated sugar, cocoa powder, and light brown sugar for the topping.
Once the butter has melted completely, spread the dough mixture evenly over the bottom of the baking dish. Do not stir the mixture; just ensure that the butter coats the bottom of the pan.
Sprinkle the topping mixture evenly over the dough.
Carefully pour the boiling water over the topping mixture, without stirring or mixing.
Bake in the preheated oven for 35-40 minutes, until the top is set and cracked, but the center is still slightly jiggly.
Remove from the oven and let it cool for 15 minutes before serving.