In a small heavy saucepan, whisk together the granulated sugar and eggs until thoroughly combined.

Cook over low heat while whisking constantly until the mixture reaches an internal temperature of 160°F (71°C) and thickens enough to coat the back of a spoon.

Remove the saucepan from heat and stir in the melted chocolate until the mixture is smooth. Set aside to cool to room temperature.

In a stand mixer bowl, cream the softened butter on medium-high speed until light and fluffy, approximately 3 minutes.

Gradually pour the cooled chocolate mixture into the butter while beating continuously.

Continue to beat the mixture on medium-high speed for 5 minutes until the texture is light, airy, and silk-like.

Beat in the vanilla extract until incorporated.

Transfer the chocolate filling into the pre-baked pie shell and smooth the surface with an offset spatula.

Refrigerate the pie for at least 4 hours, or until the filling is firm and set.

In a chilled bowl, whisk the heavy whipping cream and powdered sugar until stiff peaks form.

Spread the whipped cream over the top of the chilled pie and garnish with chocolate shavings before serving.