In a mixing bowl, whisk together the eggs and sugar until the mixture is pale and frothy.

In a medium saucepan, combine the milk and heavy cream and heat over medium heat until just steaming.

Slowly pour a small amount of the hot milk mixture into the egg mixture while whisking constantly.

Gradually whisk the tempered egg mixture back into the saucepan with the remaining milk and cream.

Cook the mixture over low heat, stirring constantly until it thickens slightly and coats the back of a spoon.

Remove the saucepan from heat and stir in the vanilla extract and ground nutmeg.

Transfer the eggnog to a bowl or pitcher and refrigerate for at least 2 hours, or until chilled.

Serve the eggnog in chilled glasses and garnish with a sprinkle of nutmeg or cinnamon.