Preheat oven to 160 degrees celsius (fan-forced). Grease a large (6 cup capacity) baking dish and set aside.
Melt the butter in the microwave in a microwave-safe bowl on 50% power for 2 minutes or until melted. Allow to cool slightly.
Add the milk, vanilla extract, egg and Baileys and whisk together.
Sift the self-raising flour and cocoa powder over the liquid mixture. Add the caster sugar and whisk together until combined.
Pour the mixture into the prepared baking dish.
Sprinkle the extra cocoa powder and caster sugar over the pudding mixture.
Carefully pour over the Baileys Irish cream and boiling water.
Bake for 30 minutes or until firm on the top (but liquid underneath - as this is the sauce).
Allow to cool slightly, then dust with icing sugar.
Serve with vanilla ice-cream or custard.