Combine the eggs and sugar in a medium bowl and whisk until thoroughly combined. Transfer to a saucepan and stir in whole milk, vanilla extract, and ground nutmeg.

In a separate bowl, stir the half and half and evaporated milk until combined.

Heat the egg mixture over medium-low heat, stirring constantly to keep the milk from scorching. When mixture reaches 160 degrees on a candy thermometer, remove from heat and slowly whisk in the evaporated milk mixture.

Allow the eggnog to cool slightly before tasting. Adjust the taste by adding more sugar or nutmeg, if desired, before pouring into a pitcher or container and cover tightly. Refrigerate overnight or until thoroughly chilled. Serve in mugs and garnish with whipped cream, cinnamon sticks, or a dash of nutmeg.