In a heatproof bowl, combine cocoa powder, sugar, starch and salt and set aside.
Pour milk into a saucepan and heat to a high temperature over medium heat, but do not bring to a boil.
Pour some hot milk into a bowl of cocoa, stir, and then put this chocolate paste in a saucepan with the remaining milk on the stove over low heat. Add the egg and half of the butter, stir well.
Cook the pudding over low heat for about 5-8 minutes, stirring constantly. Then remove the saucepan from the stove, add the vanilla extract and the remaining butter, stir well.
Serve the chocolate pudding in a serving bowl, drizzle with cream.