Whisk the milk, granulated sugar, cocoa, cornstarch, salt and egg yolks in a heavy saucepan until smooth.
Cook over medium heat, whisking constantly, until the custard boils, then continue for 1 minute.
Remove from the heat, stir in the chocolate, butter and vanilla until smooth, and pour into the cooled crust.
Press parchment directly on the filling and refrigerate for at least 5 hours.
Beat the cream and powdered sugar to soft peaks, spoon it over the chilled pie in a simple uneven layer, and slice with a hot dry knife.