Mix sugar, rum, bourbon, brandy, salt, vanilla extract, and nutmeg in a blender on medium speed until combined. Transfer liquor mixture to a large bowl.
Mix half-and-half, cream, and eggs in the blender on low speed until combined. Stir egg-cream mixture into theliquor mixture.
Ladle eggnog mixture into the blender in batches; blend on low speed. Transfer blended eggnog to a punch bowl or pitcher. Refrigerate until cold, 1 to 2 hours.
This recipe contains raw egg. We recommend that pregnant women, young children, the elderly, and the infirm do not consume raw egg. Learn more about egg safety from our article, How to Make Your Eggs Safe.
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