Pour the remaining 1 1/3 cups (320 ml) milk with the cream into a medium-sized heavy saucepan. Bring this mixture just to a boil (the milk will start to foam up) and then remove from heat. Gradually pour the hot milk into the egg mixture, whisking constantly, until the mixture is smooth. Transfer the pudding mixture to a clean, heavy bottomed medium sized saucepan and place over medium-low heat. Cook, stirring constantly, until the mixture thickens to the consistency of mayonnaise (about 3 - 5 minutes). Remove from heat and pour through the strainer to remove any lumps that may have formed during cooking. Add the finely chopped chocolate, vanilla extract, and butter, stirring gently with a rubber spatula until the mixture is smooth. Cover with plastic wrap, to prevent a skin from forming, let cool, and then chill in the refrigerator until thick (for at least four hours, or even overnight).
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