Combine milk, sugar, and cinnamon stick in a small, heavy saucepan over medium-low heat; cook 5 minutes or just until sugar dissolves and mixture is hot, stirring occasionally.
Place egg yolks in a medium bowl; stir with a whisk until blended. Gradually add about half of hot milk mixture, stirring constantly with a whisk (leave cinnamon in pan). Add egg mixture to milk mixture in pan. Cook over medium-low heat 6 minutes or until the mixture thickens and coats the back of a spoon, stirring constantly with a wooden spoon (do not boil).
Strain sauce through a fine sieve into a bowl; discard cinnamon. Place bowl of sauce in a large ice-filled bowl for 15 minutes or until sauce is room temperature, stirring occasionally. Cover and chill.