In a medium saucepan, combine the root beer and cornstarch. Whisk until the cornstarch is dissolved. Place over medium heat and bring to a boil. Reduce heat and simmer for 1 minute.
Add the brown sugar and whisk until dissolved. Slowly add the egg yolks, whisking constantly. Cook for 1 minute.
Remove from heat and stir in the butter and vanilla extract.
Pour into the prepared graham cracker crust. Cover with plastic wrap and refrigerate for at least 2 hours.
Just before serving, whip the cream with an electric mixer until stiff peaks form. Spread over the chilled pie.