In a medium saucepan whisk together the milk and heavy cream. Heat over medium heat, whisking occasionally, until small bubbles form around the edges but do not let the mixture come to a boil.
In a small bowl whisk together the sugar, cornstarch and salt. Add to the milk mixture, whisking to combine.
Remove the saucepan from heat and add the chocolate, stirring constantly until it’s completely melted. Return to medium-low heat if needed.
Divide among cups and top with whipped cream and additional chocolate shavings. Serve immediately.