Heat oven to 350°F (175°C). Grease a 9×9-inch baking dish with butter or nonstick spray.
Whisk melted butter, brown sugar, granulated sugar, and vanilla in a large bowl. Stir in the milk.
In another bowl, sift flour, baking powder, salt, and cocoa powder. Add to the wet mixture and stir until just combined. Fold in chocolate chips, then spread the batter evenly in the dish.
Mix granulated sugar and cocoa powder in a bowl. Sprinkle it evenly over the batter without stirring.
Slowly pour hot water over the topping. Do not mix—let it sit on top.
Bake for 40–45 minutes until the top is firm, edges are bubbly, and the center is slightly soft. Let it rest for 5–10 minutes. Scoop into bowls, making sure to include the gooey sauce.