In a medium saucepan, whisk together the milk, sugar, cornstarch, and cocoa powder. Bring to a simmer, stirring constantly, until the mixture thickens.
Remove from the heat and stir in the butter and vanilla extract.
Pour the mixture into the prepared pie crust and chill for at least 2 hours.
In a medium bowl, whip the cream and powdered sugar until stiff peaks form. Fold in the brandy and spread over the chilled pie.
Chill for at least 1 hour before serving.
Interesting Facts
The classic Brandy Alexander cocktail is made with equal parts brandy, crème de cacao, and cream.
The Brandy Alexander Pie was created by the pastry chef at the Waldorf-Astoria Hotel in New York City.
The Alexander Pie is also known as "Millionaire Pie" due to its luxurious ingredients.