Whip heavy cream to stiff peaks using an electric mixer on medium-high speed for 2-3 minutes. Transfer to a bowl and refrigerate.

Combine eggs, sugar, and water in a heatproof bowl set over a saucepan of simmering water (double boiler, ensure bowl doesn't touch the water).

Beat the egg mixture with an electric mixer on medium speed until thickened and reaches 160°F (7-10 minutes).

Remove the bowl from heat and continue beating until the egg mixture is fluffy and cooled to room temperature (about 8 minutes).

Add melted and cooled bittersweet chocolate and vanilla extract to the egg mixture. Beat until well combined.

Gradually beat in softened butter pieces, a few at a time, until fully incorporated.

Gently fold in the whipped cream with a spatula until no white streaks remain.

Pour the chocolate filling into the baked and cooled pie shell.

Refrigerate the pie for at least 3 hours, or up to 24 hours, to allow the filling to set completely.

Serve chilled.