While the crust is cooling, bring a small pot filled with 2 inches of water to a simmer over medium heat. In a heat-proof bowl, whisk together sugar and eggs. Place the bowl on top of the pot, making sure the bottom doesn’t touch the water. (The bowl should be large enough to rest on top of the pot.)
Cook, stirring constantly, until the mixture reaches 160F or until it feels warm to the touch and completely smooth when rubbed between your fingers. Remove from the pot.
Add the chocolate and vanilla. Gently whisk until completely melted and the mixture is smooth. It will likely thicken as you stir, turning into a pudding-like consistency. Let cool, stirring occasionally, until the mixture doesn’t feel warm but isn’t solidified, about 30 minutes.
In a large mixing bowl, beat the butter on medium speed until smooth and fluffy, about 2 minutes. Add the cooled chocolate mixture. Beat on medium speed until very fluffy, and soft shiny peaks form, about 3 minutes.
In a separate bowl, beat the cream on medium speed until soft peaks form. Fold the whipped cream into the whipped chocolate mixture until no white streaks remain. Pour into the cool pie shell.
Refrigerate for at least 3 hours or up to a day.