In a mixing bowl, whisk the eggs and sugar together until pale and frothy.

In a saucepan over medium heat, combine the milk and heavy cream and heat until steaming but not boiling.

Slowly pour the hot milk mixture into the egg mixture while whisking continuously.

Return the mixture to the saucepan and cook over low heat, stirring constantly until thickened, about 5 minutes.

Remove from heat and stir in the bourbon, vanilla extract, and nutmeg.

Let the eggnog cool to room temperature, then cover and refrigerate for at least 2 hours.

Pour the chilled eggnog into glasses, straining it through a fine mesh strainer if desired.

Sprinkle extra nutmeg on top before serving.