Bake the unbaked 9-inch pastry crust according to its recipe or package directions until fully golden, using pie weights during the first part of baking if blind-baking. A typical bake is about 15–20 minutes at 375°F; cool the crust completely before adding the filling.

Whisk the sugar, cocoa powder, flour, and salt together in a medium saucepan. Gradually whisk in the whole milk until the mixture is smooth and free of lumps.

Cook the mixture over medium heat, whisking frequently, until it thickens and begins to bubble. Continue cooking for about 1–2 minutes after bubbling begins, making sure the pudding coats a spoon.

Lightly whisk the egg yolks in a separate bowl. Slowly whisk approximately 1 cup of the hot chocolate mixture into the yolks to temper them, then return the tempered mixture to the saucepan.

Cook over medium-low heat for 1–2 minutes while stirring constantly. Do not let the custard boil vigorously, or the egg yolks may curdle.

Remove the saucepan from the heat and stir in the butter and vanilla. For an especially smooth filling, strain the pudding through a fine-mesh sieve.

Pour the hot filling into the cooled crust and press plastic wrap directly against the pudding surface. Refrigerate for at least 4 hours, preferably overnight, until the pie is completely set.

Whip the heavy cream with the powdered sugar and vanilla until soft or medium peaks form. Spread or pipe the cream over the chilled pie just before serving.