Start some water boiling in the kettle so that it is ready for you.
Mix together the egg, milk, butter and vanilla in a bowl.
Sift into another bowl the flour, sugar, 2 tablespoon of the cocoa and a dash of salt. Mix together, then make a well in the middle, and pour in all the milk mixture, then whisk the milk into the flour a bit at a time until you have an even, thick batter. You don't have to be really delicate with this; it shouldn't take you more than half a minute.
Mix remaining cocoa with the brown sugar in a separate bowl or cup until there are no sugar lumps left, and set aside.
Spoon the pudding batter into a baking dish that will hold 2 ½ pints (5 cups / 1.5 litres), and level it out with the back of a spoon. Sprinkle the brown sugar and cocoa mix over top of the pudding.
Carefully pour 1 ¼ cups (10 oz / 300 ml) of boiling water onto the pudding. You want the pudding dish to end up about ¾ full of pudding and water. (Don't go any higher or it will all bubble out on you.) Use a bit more or less water as needed depending upon your dish.
Bake for around 45 minutes, until firm and risen. Remove from oven, dust with the icing sugar through a sieve, and serve.
Notes
Instead of the flour, salt and baking powder, you may use 1 ¼ cup (5 oz / 150g) of self-rising flour.Optional: a tablespoon of something nice like Kahlua, Bailey's Irish Cream, brandy, or whatever you think might be nice in the way of booze and flavouring.