Besides being a revelation in deliciousness, homemade eggnog is made with just five ingredients — four if you leave out the booze. Compare this to the laundry list of additives in most commercial brands of eggnog. Most of those additives are there to artificially thicken the eggnog and give it a longer shelf-life — but if you make your eggnog at home, you don't need to worry about any of this.
Separate the eggs: Separate the eggs, placing the yolks in one bowl and the whites in another (I recommend the 3-Bowl Method for this step). Cover the whites and refrigerate until needed (or freeze if aging the eggnog for longer than a day).
Whisk the yolks with the sugar: Combine the yolks and the sugar in a medium mixing bowl. Whisk by hand, or with a mixer, until the mixture is smooth and creamy, and it has lightened to a lemon-yellow color
Whisk in the milk, cream, and liquor (if using): Pour the milk, cream, and liquor into the bowl with the egg mixture and whisk until combined.
Cover and refrigerate: Cover the bowl and chill in the refrigerator for at least an hour. The more liquor you add, the longer it will keep — non-alcoholic eggnog should be consumed within a day; eggnog with 1/2 to 1 cup of liquor will keep for several days; and eggnog with 1 1/2 cups of liquor will keep for several weeks and continue aging and thickening quite nicely. (If aging for longer than a few days, transfer the eggnog to a sealed glass container or a mason jar.)
Whisk the egg whites: Just before serving, whisk the reserved egg whites in a stand mixer or with a hand mixer at high speed until the whites form stiff peaks.
Fold the egg whites into the eggnog: Transfer the beaten egg whites to the bowl with the eggnog and gently fold or stir the whites into the base — this gives the eggnog a frothy, extra-creamy texture. Some of the egg whites will also float to the top, like cappuccino foam.
Serve the eggnog: Transfer the eggnog to a pitcher or punch bowl. Serve in individual glasses with a grating of nutmeg over top.