In a saucepan, combine the milk and heavy cream. Heat the mixture over medium-low heat until it reaches a gentle simmer. Stir occasionally to prevent scorching.

In a mixing bowl, whisk together the sugar and eggs until well combined and slightly frothy.

Gradually pour about a cup of the hot milk mixture into the egg mixture, whisking constantly to temper the eggs.

Pour the tempered egg mixture back into the saucepan with the remaining hot milk mixture, whisking constantly.

Cook the mixture over medium-low heat, stirring continuously, until it thickens slightly and coats the back of a spoon. Do not let it come to a boil.

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

If adding alcohol, stir it in at this stage.

Strain the eggnog through a fine-mesh sieve to remove any cooked egg bits.

Allow the eggnog to cool to room temperature, then cover and refrigerate it for at least 4 hours or overnight to chill completely.