Beat sugar and egg yolks together in a bowl using an electric mixer until very light in color. Mix milk and cream into yolk mixture.
Beat egg whites in a separate bowl using an electric mixer until stiff peaks form, adding more sugar, if desired. Fold egg whites into milk mixture until eggnog is smooth. Stir rum and whisky into eggnog. Refrigerate until chilled, at least 1 hour.
This recipe contains raw eggs. We recommend that pregnant women, young children, the elderly, and the infirm do not consume raw eggs. Learn more about egg safety from our article, Making Your Eggs Safe.