Combine sugar, cornstarch, and salt in a medium-sized saucepan. Stir the milk in gradually, then add the chocolate chips and chopped chocolate squares.

Place the saucepan over medium heat, stirring constantly, until the mixture thickens and boils. Boil and stir for 1 minute.

Put beaten egg yolks in a medium heatproof bowl. Gradually pour half of chocolate mixture into egg yolks, whisking constantly.

Whisk egg yolk mixture back into the mixture in the saucepan. Place over medium heat and bring back to a boil, stirring constantly. Boil and stir for 1 minute. Remove from heat; stir in vanilla extract.

Pour mixture into baked pie shell. Press a layer of plastic wrap onto filling. Refrigerate at least 4 hours but no longer than 48 hours. Remove plastic wrap before serving and top with whipped cream and optional chocolate shavings for garnish.