Whisk Egg Yolks and Sugar:

In a medium mixing bowl, whisk the egg yolks and sugar together until the mixture is light and creamy.

Heat Milk Mixture:

In a saucepan, combine the milk, heavy cream, and nutmeg. Heat over medium heat until the mixture is warm but not boiling, stirring occasionally.

Temper the Eggs:

Slowly pour a ladleful of the warm milk mixture into the egg yolk mixture, whisking constantly to temper the eggs. Repeat this process with another ladleful of warm milk.

Cook the Eggnog Base:

Pour the tempered egg yolk mixture back into the saucepan. Cook over medium heat, stirring constantly, until the mixture thickens slightly and coats the back of a spoon (about 160-170°F or 70-75°C). Do not let it boil.

Add Flavorings:

Remove the saucepan from heat and stir in the vanilla extract and optional alcohol. Strain the mixture through a fine mesh sieve to ensure a smooth texture.

Chill:

Transfer the eggnog to a pitcher or container and refrigerate for at least 4 hours, or until fully chilled.

Serve:

Pour the eggnog into glasses, top with whipped cream if desired, and sprinkle with additional nutmeg for garnish.