FOR BASE: In a heavy medium-sized saucepan, barely boil the milk with the vanilla bean, which has been split lengthwise, scraped with the back edge of a knife and added to the milk--seeds, pod, and all (if using vanilla extract, you'll add it after eggnog base has cooked).
Meanwhile, place a large fine-mesh strainer over a bowl set in a large bowl of ice.
Beat the yolks and sugar together in the top of a double boiler, by hand or with electric beaters, until thick and smooth, about 1 minute.
Whisk in the hot vanilla milk.
Cook in the double boiler set over simmering water, stirring constantly all around the bottom and corners with a rubber or wooden spatula.
In time, foam will subside.
The eggnog base is done when it coats a wooden spoon without bare spots, 12 to 15 minutes.
Immediately pour through strainer, stirring to cool.
When cool to the touch, slowly whisk in all liquors (if using vanilla extract instead of vanilla bean, add this now, too).
Store eggnog base in refrigerator overnight or up to three days, to ripen.
TO COMPLETE EGGNOG: At serving, remove vanilla bean and pour eggnog base into a large punch bowl.
Beat egg whites with 3 tablespoons sugar to stiff peaks; fold into eggnog mixture.
Beat cream to stiff peaks and fold it in, too.
Let some lumps of the cream and egg whites float on surface.