For the cake: Preheat the oven to 350 degrees F. Line the bottoms of both cake pans with parchment paper and butter the sides.
Put the cocoa and 1/2 cup dark brown sugar into a bowl with a bit of space to spare, and pour in the boiling water. Whisk to mix, then set aside.
Cream the butter and superfine sugar together, beating well until pale and fluffy; I find this easiest with a free-standing mixer, but by hand wouldn't kill you.
While this is going on - or as soon as you stop if you're mixing by hand - stir the flour, baking powder and baking soda together in another bowl, and set aside for a moment.
Dribble in the vanilla extract into the creamed butter and sugar - mixing all the while - and then drop in an egg, quickly followed by a scoopful of the flour mixture, then add the second egg.
Keep mixing and incorporate the rest of the dried ingredients for the cake then finally mix and fold in the cocoa mixture, scraping its bowl out well with a spatula. Divide this fabulously chocolatey batter between the two prepared pans and put in the oven for about 30 minutes, or until a cake tester comes out clean. Take the pans out and put them on a wire rack for 5 to 10 minutes, before turning the cakes out to cool.
But as soon as the cakes are in the oven, get started on your frosting: put the water, 2 tablespoons dark brown sugar and 1 1/2 sticks butter in a pan over low heat to melt.
When this mixture begins to bubble, take the pan off the heat and add the chopped chocolate, swirling the pan so that all the chocolate is hit with heat, then leave for a minute to melt before whisking till smooth and glossy.
Let it stand for about 1 hour, whisking now and again - when you're passing the pan - by which time the cakes will be cooled, and ready for the frosting.
Set one of the cooled cakes, with its top side down, on a cake stand or plate, and spread about a third of the frosting, then top with the second cake, regular way up, and spread the remaining frosting over the top and sides, swirling away with your spatula. You can go for a smooth look, but I never do and probably couldn't.
Make Ahead Note: The cake layers can be baked 1 day ahead and assembled before serving: wrap tightly in plastic wrap and store in airtight container. Iced cake will keep for 2 to 3 days in airtight container in a cool place.
Freeze Note: Un-iced cake layers can be frozen on day of baking, each wrapped in double layer of plastic wrap and a layer of aluminium foil, for up to 3 months. Thaw for 3 to 4 hours on wire rack at room temperature.