Combine milk, sugar, cocoa powder, and cornstarch in a bowl and mix well.
Pour the mixture into a saucepan and simmer over low heat, stirring constantly.
When thickened, remove from heat and add chopped chocolate, stirring until melted.
Strain the finished pudding through a sieve to make it smooth.
Pour into containers and chill in the refrigerator for at least 2 hours.