Preheat oven to 350°F (175°C). Lightly grease a 9-inch square baking pan*. Pre-boil water in a kettle while preparing cake.: The warm oven gives you consistent rising and golden edges, and greasing the pan prevents sticking so the cake releases smoothly. You should feel a small hum of heat as you open the oven, and the smell of warm metal is reassuring. If the oven is cooler than indicated, the cake will bake slower and the pudding may be overly loose; use an oven thermometer for accuracy.
Combine 1/2 cup granulated sugar with the flour, cocoa powder, baking powder and salt. Add in the milk, butter and vanilla; whisk until smooth and fairly lump free.: Having boiling water ready ensures the sauce forms immediately when poured, preserving the contrast between the batter and the pudding. The kettle's whistle is a useful cue that you are ready for the step. If the water is not fully boiling, the sauce may be less glossy and not as fully dissolved, so keep it at a rolling boil until use.
Pour the batter into prepared baking pan or dish and spread evenly.: The dry mix should smell faintly of cocoa and have a light, dusty texture as you whisk. Doing this first distributes leavening and cocoa, preventing pockets of taste or uneven rise. A common pitfall is underwhisking which leads to lumps or uneven flavor, so break up any clumps with a fork or sieve.
Combine together the remaining 1/2 cup white sugar, brown sugar and remaining 3 tablespoons cocoa powder. Evenly sprinkle mixture over the batter. Slowly pour the boiling water over the top (DO NOT STIR OR MIX INTO THE BATTER. ALLOW THE WATER TO SIT ON TOP).: The batter should be glossy and pourable, with the aroma of warm butter and chocolate brightened by vanilla. Vigorously whisking creates a silken batter without overworking the gluten. Overmixing can toughen the cake, so stop once the batter looks homogeneous and slightly thick but still ribbon like when lifted with a spoon.
Bake 35 minutes or until the centre is almost set. Remove from oven. Allow to cool for 15 minutes.: As you smooth the batter, it should level out and form an even surface. The batter will look slightly glossy and set the stage for an even cake rise. Bumping the pan on the counter a few times releases large air bubbles, but avoid aggressive shaking that can deflate the batter.
Serve in dessert dishes with ice cream or whipped cream, and spoon fudge sauce from the bottom of pan over top of each serve of cake.: This topping blend should smell more robustly chocolatey and slightly caramel like from the brown sugar. Evenly distributing these dry ingredients over the batter ensures the sauce forms uniformly beneath the cake. If you pile the mixture in one spot, the pudding will be uneven, so sprinkle carefully for consistent results.
Evenly sprinkle mixture over the batter.: As the sugar and cocoa settle on the batter, they create a thin layer that will dissolve into the sauce when the boiling water is added. The visual is a dusty chocolate blanket covering the pale batter, and it helps to use the back of a spoon to spread if needed. Avoid stirring it in, as mixing will ruin the separation that creates the pudding layer.
Slowly pour the boiling water over the top (DO NOT STIR OR MIX INTO THE BATTER. ALLOW THE WATER TO SIT ON TOP).: You will hear a soft hiss as the water hits the dry topping, and the aroma of hot chocolate intensifies. This step dissolves the topping and causes the heavier syrup to sink during baking, forming the pudding below. Stirring now will incorporate the water and prevent the layered texture, so resist the urge to mix.
Bake 35 minutes or until the centre is almost set.: The oven will fill with a deep chocolate scent, and the cake top should look set and slightly springy while the centre remains just a touch jiggly. This borderline doneness is important because residual heat finishes the pudding without drying it. Overbaking will dry out the cake and reduce sauce, so check at the lower end of the time range and trust the visual cues.
Remove from oven. Allow to cool for 15 minutes.: Cooling lets the pudding thicken slightly and makes serving easier. As it rests you will notice the sauce settling and the steam calming, which helps concentrated flavors develop. Cutting or serving too hot can lead to a runnier presentation, so patience yields the ideal saucy texture.
Serve in dessert dishes with ice cream or whipped cream, and spoon fudge sauce from the bottom of pan over top of each serve of cake.: The first spoonful should pair the warm, glossy sauce with cold, creamy ice cream for a satisfying contrast of temperature and texture. Spoon from the pan carefully so each portion gets both cake and sauce. A common mistake is scooping from the top only, missing the luscious sauce hiding below, so dig slightly to capture both layers.