Preheat your oven to 350°F (175°C). Grease a 9-inch square baking dish.
In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, salt, and 1/4 cup cocoa powder until well combined.
Add the milk, vegetable oil, and vanilla extract to the dry ingredients. Stir until the batter is smooth and well mixed.
Pour the batter into the prepared baking dish, spreading it evenly.
In a separate bowl, mix the brown sugar and 1/4 cup cocoa powder. Sprinkle this mixture evenly over the batter in the baking dish.
Carefully pour the hot water over the top of the dish. Do not stir; the water will create a fudge sauce underneath the cake as it bakes.
Bake in the preheated oven for 40-45 minutes, or until the top is set and a toothpick inserted into the cake part comes out clean.
Let the cake cool for about 10 minutes before serving. Serve warm, spooning the fudge sauce from the bottom over each portion.