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Strain the milk mixture through a sieve into a bowl. Discard the solids and return the milk to the pan. Stir in the sugar, cornstarch, cocoa and salt. Return the pan to medium heat and bring to a boil, stirring constantly with a whisk until the mixture thickens.
Put the egg yolks in a medium bowl and gradually add half of the hot milk mixture, stirring constantly with a whisk. Add the egg mixture to the pan and bring to a boil, stirring constantly. Cook until thick, 1 minute. Off the heat, add the chocolate and vanilla, stirring until the chocolate melts.
Pour the pudding into a bowl and cover the surface with plastic wrap. Refrigerate until chilled.