Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x9-inch baking pan.

Whisk flour, sugar, 2 tablespoon cocoa powder, baking powder, and salt together in a large bowl. Stir in milk and butter until smooth. Fold in walnuts until just combined.

Spread batter evenly into the prepared baking pan.

Combine brown sugar and 1/4 cup cocoa powder in a small bowl; sprinkle on top of batter. Pour hot water over batter.

Bake in the preheated oven until center of cake is almost set, about 45 minutes. (Brown sugar, cocoa powder, and hot water will combine to form a chocolate sauce that will settle to the bottom of the cake during baking.) Serve it warm.