Preheat oven to 300°F/150°C, combi steam setting. If your oven has variable humidity, choose 50%/medium steam. If not, don't worry! Just set to combi steam at the correct temperature and the oven will sort out the steam level.
Lightly grease a 1.5qt/1.5L lightweight enamel baking dish, and set aside.
Whisk the brown sugar, cocoa powder and salt for the sauce in a bowl and set aside. Whisk the flour, baking powder, granulated sugar, cocoa powder and salt in a separate bowl.
1 cup brown sugar, 1/4 cup cocoa powder, 1/4 tsp flaky salt, 1 1/4 cups all-purpose flour, 2 1/2 tsp baking powder, 1/3 cup granulated sugar, 1/4 cup cocoa powder, 1/2 tsp flaky salt
In a small jug, whisk together the melted butter, milk, egg and vanilla.
1/2 cup whole milk, 4 Tbsp unsalted butter, 1 egg, 1 tsp vanilla extract
Pour the egg mixture into the flour mixture and mix with a spatula until combined It will be a thick batter, this is normal.
Spread the batter into your baking dish and smooth out the top. Sprinkle with sugar and cocoa mixture, then shake gently to even out this layer.
Carefully pour the boiling water over the back of a soup or dessert spoon, all over the top of the pudding - see notes.
1 1/4 cups boiling water
Carefully place into the oven and bake until the top of the pudding springs back when poked lightly and the underneath seems 'jiggly', about 20 minutes. Don't overbake or you'll end up with no sauce.
Remove from oven and let it stand for 2-3 minutes, then serve immediately, scooped into bowls with cream or ice cream on top.