Heat milk with cinnamon stick until steaming. Remove from heat and steep for 15 minutes. In a separate saucepan, whisk together yolks until frothy. Stir in sugar, whisking, over medium low heat until mixture is gold and thick. Slowly dribble in the hot milk stirring constantly with a wooden spoon. Allow sauce to simmer but not boil, otherwise the eggs will solidify. Cook for a few minutes more. The sauce will be finished when it can coat a spoon in a creamy layer, and will hold a line when a finger is drawn across it. Stir in the vanilla extract at the end and serve.