Heat the milk and cream in a small saucepan until small bubbles appear around the edges.
Combine the sugar, cornstarch and salt in a medium saucepan and stir until blended.
Add the hot-milk mixture and heat over medium-low heat, stirring, until it begins to thicken and boil.
Add the chocolate.
Cook, stirring slowly and constantly, until the mixture boils and the chocolate is melted.
Whisk the egg yolks in a small bowl.
Add a spoonful of the hot-milk mixture to the eggs and stir to blend.
Stir the egg mixture back into the saucepan.
Cook over low heat, stirring, for 2 minutes, or until the pudding is thickened and reaches 165 to 170 degrees.
Set a sieve over a bowl and strain the pudding.
Push the last drops of pudding through and scrape the underside of the sieve with a rubber spatula.
Stir in the vanilla.
Transfer the pudding to a serving bowl or individual pudding cups or dessert dishes.
Serve warm, at room temperature or chilled.