Put the milk in a microwaveable jug with the chocolate pieces and microwave on high for 60 seconds. Stir and set side to cool.
Beat the butter and sugar in a mixing bowl until fluffy and light. Beat in the eggs, then fold in the flour, cocoa powder, and vanilla extract. Fold it through well, making sure to fold in the bits at the bottom of the bowl, then fold in the warm chocolate milk.
Grease your microwaveable pudding bowl (size approx 750ml/1.5 pints) spoon in the pudding batter, and level off the top with the back of a spoon. Cover tightly with clingfilm and microwave on high for 5 mins 30 secs. Rest for a few mins before turning out into a plate.
Heat the milk in a jug or bowl in the microwave on full for ⅚ mins and near boiling point.
While that's cooking, put the egg yolks and all the remaining ingredients into a microwaveable bowl/jug or saucepan large enough to hold these ingredients plus the milk (approx 1 litre). Mix well into a paste with the additional 2 tbsp milk.
When the milk is hot, whisk into the paste until fully mixed, then put the pan on the hob on a medium heat stirring regularly until thick or if microwaving pop it in the microwave for 90 secs. Remove and whisk and pop it back in the microwave for 1 min, whisk again and back into the microwave for another min and repeat until the custard thickens (⅘ times)