Heat milk in a medium saucepan over medium heat just until bubbles and steam appear (do not boil). Remove from heat.
Whisk together sugar and egg yolks in a medium bowl until blended. Gradually add heated milk to egg yolk mixture, whisking constantly. Return mixture to saucepan. Cook over medium heat, whisking constantly, 6 minutes or until mixture thinly coats the back of a spoon. Pour mixture into a bowl. Stir in vanilla. Place plastic wrap directly on surface of mixture, and chill at least 4 hours. (Mixture will thicken slightly as it cools.) Stir in bourbon before serving.