Separate 6 large eggs into yolks and whites
In a saucepan, whisk 1 cup sugar into the 6 yolks
Whisk in 2 cups milk and 1 cup heavy cream
Cook over medium-low heat, stirring constantly, until thickened and coats the back of a spoon (about 160–170°F / 71–77°C)
Remove from heat
Stir in 1/2 teaspoon ground nutmeg and 1/2 teaspoon vanilla extract (optional: additional nutmeg for serving)
Let the mixture cool to room temperature
Whip the 6 egg whites to soft peaks
Fold the whipped egg whites into the cooled eggnog
Add 1/2 to 3/4 cup rum, bourbon, or brandy (optional) and stir
Chill at least 4 hours, preferably overnight
Serve cold, topped with a pinch of nutmeg