French Silk Pie

Preheat the oven to 375 degrees F (190 degrees C).

Beat 1 egg in a bowl; brush over entire pie crust surface, including edges. Prick holes into bottom and sides of crust with a fork.

Bake in the preheated oven until golden brown, 10 to 15 minutes. Cool completely, about 30 minutes.

Combine white sugar and remaining 2 eggs in a medium saucepan over medium-low heat; stir continuously, adjusting heat as needed to make sure it does not boil or bubble, until mixture coats the back of a spoon and an instant-read thermometer reads 160 degrees F (70 degrees C), about 10 minutes.

Off heat, stir in melted chocolate and vanilla extract; cool to lukewarm temperature, 15 to 20 minutes.

Beat butter in a separate large bowl using an electric mixer until light and fluffy; add chocolate mixture. Continue to beat on high speed until thick and creamy, about 5 minutes.

Beat cold heavy cream in a separate bowl until slightly thick. Add confectioners' sugar all at once; continue to beat on medium to medium-high speed until stiff peaks form. Fold into chocolate mixture, stirring very gently so as not to decrease the volume by stirring too much. Pour into the prepared pie crust; chill in the refrigerator for at least 2 hours before serving.