Preheat oven to 350°F (Gas Mark 4), grease and line an 8×8-inch tin with parchment.
Beat butter and sugar until pale and fluffy.
Add eggs one at a time with vanilla, mixing well.
Sift in flour and cocoa, gently fold to combine.
Add milk for a soft batter, pour into tin, and smooth top.
Bake 25–30 minutes until springy; cool slightly.
Mix cornflour, sugar, and cocoa with milk; whisk into hot milk, cook until thick, then add vanilla.
Cut sponge, top with hot chocolate custard, and serve warm.