Cover and refrigerate the egg whites.
In a mixing bowl, briskly whisk together the 6 egg yolks and the sugar until light yellow and airy, about 90 seconds. Pour in the bourbon, rum, and cognac. Gently whisk the liquors into the egg yolk mixture until well combined, helping the sugar dissolve as your whisk. Stir in the milk and cream until smooth. Transfer the eggnog to a covered pitcher and refrigerate at least 1 hour (or overnight).
When ready to serve, whip the egg whites until a soft peak forms. Begin by folding 1/4 of the egg whites into the chilled eggnog. If you like your eggnog more frothy, fold in more egg whites gradually until desired frothiness is achieved. Pour the eggnog into short glasses. Sprinkle with nutmeg. Serve. Leftover eggnog can be kept, sealed in a mason jar, in the refrigerator for up to 3 weeks. Recipe adapted from The Kitchn.
*if you like a thicker eggnog to begin with (before aging), use heavy cream here instead of half and half, but bear in mind that it will get even thicker over time.
WARNING: This recipe contains raw eggs. Use very fresh, organic eggs if at all possible. Be aware that consuming raw or undercooked eggs can increase your risk for certain food-borne illnesses, especially if you have a medical condition.