In a medium saucepan, whisk together the eggs and sugar.
With a candy thermometer to measure temperature, heat the egg mixture over medium-low heat until it reaches 140°F. Keep the mixture at 140°F for about 5 minutes, whisking continuously. If the temperature rises about 150°F, remove the egg mixture from the heat.
Add the chocolate to the heated egg mixture and whisk to combine. Once the chocolate is melted into the mixture, set aside and let the mixture cool to room temperature.
Whisk the softened butter into the chocolate mixture until smooth. Add the vanilla extract and whisk to combine.
In a separate bowl, using either a stand mixer fitted with the whisk attachment or an electric hand mixer, mix the heavy cream on high until it becomes light and fluffy.
Fold the unsweetened whipped cream into the chocolate mixture until no streaks remain.
Transfer the chocolate pie filling into the prepared pie crust and refrigerate until chilled and set, at least 4 hours or overnight.