Break the 8 ounces bittersweet chocolate bars up into pieces and microwave at 20-second intervals, stirring between each one, until fully melted. Set aside.
In a medium bowl, beat 1¼ cups heavy cream and ¼ cup powdered sugar together with a hand mixer until stiff peaks form. Transfer to the refrigerator to chill.
Whisk together 1 cup granulated sugar and 4 large eggs constantly in a small saucepan over medium heat and cook to 160°F.
Remove from heat and add in the melted chocolate. Set aside.
In a stand mixer fitted with a paddle attachment, cream the ¾ cup unsalted butter and 1 tablespoon vanilla bean paste for 3 minutes.
Switch to a whisk attachment, and slowly add in the cooled chocolate and egg mixture while the mixer mixes on the "stir" setting.
Once all of the mixture is added, increase speed to medium-high and beat for an additional 5 minutes.
Fold the chilled whipped cream into the mixture with a rubber spatula.
Pour the filling into the prepared pie crust and transfer to the refrigerator to set for at least 6 hours, preferably overnight.