Melt the Butter: Preheat your oven to 350°F (175°C). Place the 6 tablespoons of unsalted butter directly into an 8-inch square baking dish and set the pan inside the warming oven. Let the butter melt completely while the oven finishes preheating, then carefully remove the hot dish.
Whisk the Batter: In a medium bowl, sift together the self-rising flour, ¾ cup of the white sugar, and 1 ½ tablespoons of cocoa powder. Pour in the milk and vanilla extract, stirring gently until you have a smooth, thick batter.
Mix the Dry Coating: In a separate small bowl, whisk together the remaining 1 cup of white sugar and ¼ cup of cocoa powder until perfectly uniform and free of dark cocoa lumps.
Layer (Do Not Stir!): Pour the thick cake batter directly over the melted butter in the hot baking dish. Use a spatula to spread it gently, but do not stir it into the butter. Next, sprinkle the sugar-cocoa dry mixture evenly across the entire surface of the batter.
Add the Water: Slowly and carefully pour the 1 ½ cups of boiling water over the top of the entire pan. To prevent washing away the sugar-cocoa layer, pour the water gently over the back of a spoon. Do not stir. The pan will look messy and incredibly liquidy—this is exactly how it should look.
Bake: Slide the dish into the preheated oven and bake for 30 minutes. The top cake layer should be puffed up and set, while the hot chocolate sauce bubbles up along the edges of the pan.
Serve Warm: Remove from the oven and let it sit for 5–10 minutes to allow the molten fudge sauce underneath to thicken slightly. Spoon the warm cake and underlying fudge sauce directly into bowls.