Stir together 2 cups of the milk, 1/4 cup of the sugar and the 3 tablespoons cornstarch in a large saucepan. Bring to boiling. Boil gently for 1 to 2 minutes. Remove from heat; set aside.
Whisk together egg, egg yolks, remaining 1/4 cup milk, 1/4 cup sugar, the cocoa and salt in small bowl. Stir in a little of hot milk mixture. Stir egg mixture into saucepan. Cook, stirring constantly with wooden spoon, over medium-low heat until thickened and barely boiling. Remove from heat. Stir in chopped chocolate, butter, rum and vanilla.
Pour into individual serving dishes; cool 10 minutes. Cover with plastic wrap. Refrigerate at least 2 hours before serving. Top with whipped cream, if desired. Makes 4 servings.