Mix together sugar and cornstarch in a medium saucepan until well blended. Stir in milk gradually. Turn heat to medium and stir constantly until boiling. Remove from heat.

Add chocolate chips and vanilla extract to the hot milk mixture; stir until smooth and chocolate chips have melted. Transfer into a large mixing bowl, cover with plastic wrap, and place on the counter until cooled to room temperature.

Meanwhile, combine 2 cups whipping cream and powdered sugar in a large bowl; beat with an electric mixer until soft peaks form.

Uncover cooled chocolate mixture and beat with clean beater attachments until light and fluffy. Gently fold 1/2 of the whipped cream mixture into the chocolate mixture, being careful not to overmix. Spoon into pie crust and top with remaining whipped cream. Refrigerate until firm, 2 to 3 hours. Serve.