In a medium saucepan mix together the milk, cornstarch, cocoa, salt, and sugar.
Melt the chocolate in a microwave, or double boiler. Set aside to cool slightly.
Whisk the chocolate into the milk mixture, bring mixture to a boil over medium heat, reduce heat to low, and continue cooking, mixing with a rubber heat proof spatula, or wooden spoon, scraping the edge of the pan to incorporate all the ingredients. Cook for 2 minutes – mixture will be thick on glossy.
Remove from heat and mix in the vanilla. Pour the pudding mixture into a heat proof bowl though a fine strainer, pressing lightly with a spatula to eliminate any solid materials; discard solids. Cover the pudding directly on top with plastic wrap to keep skin from forming on top of the pudding.
Cool for at least 4 hours before serving; will keep for 2 days.