In a large mixing bowl, whisk together the eggs and sugar until pale and thick.
Gradually add in the milk, cream, and vanilla extract while continuously whisking.
Stir in the ground nutmeg.
If desired, add bourbon or rum to the mixture.
Transfer the eggnog to a large pitcher or bowl.
Cover and refrigerate for at least 2 hours to chill and allow flavors to meld.
Before serving, give the eggnog a good stir.
Pour into glasses and top with whipped cream if desired.
Garnish with a sprinkle of nutmeg or a cinnamon stick.
Serve chilled or gently heat for a warm version.