In a medium-size nonreactive saucepan, combine 2 cups of the milk and the sugar over medium-high heat. Bring to a boil and stir to dissolve the sugar, then reduce the heat to medium. Add the chopped chocolate and whisk until it completely melts. Remove from the heat.
Combine the egg yolks, cornstarch, and the remaining 2 tablespoons milk in a small mixing bowl and whisk until smooth. Slowly add the chocolate mixture, whisking constantly, until it is all used. Pour the mixture back into the saucepan and cook over medium heat until the mixture thickens, 3 to 4 minutes. Remove from the heat. Add the vanilla and butter and stir until the butter melts.
Pour the mixture into a glass bowl. Press a piece of plastic wrap down over the surface to prevent a skin from forming. Let cool completely. Refrigerate for 4 hours. Remove the plastic wrap and beat with a wire whisk until smooth.
To serve, spoon into dessert bowls and garnish with the whipped cream and chocolate shavings.
Yield: 4 servings