Whisk the Egg Yolks and Sugar. In a medium bowl, whisk the egg yolks and sugar together until the mixture is pale and creamy.
Heat the Milk and Cream. In a saucepan, combine the milk, heavy cream, nutmeg, and cinnamon. Heat over medium heat until steaming, but not boiling.
Temper the Egg Yolks. Slowly pour a small amount of the hot milk mixture into the whisked egg yolks, stirring constantly. This prevents the eggs from scrambling. Gradually add the tempered yolks back into the saucepan.
Cook the Eggnog. Cook the mixture over low heat, stirring constantly, until it thickens slightly and coats the back of a spoon. Be careful not to let it boil.
Add Vanilla and Chill. Remove from heat and stir in vanilla extract. Let the eggnog cool before transferring it to the refrigerator. Chill for at least 2 hours.
Serve and Garnish. Pour the eggnog into glasses, sprinkle with nutmeg, and garnish with cinnamon sticks or whipped cream. Enjoy chilled!