In a medium bowl, whisk together the egg yolks and sugar until the mixture is light and creamy.
In a saucepan over medium-high heat, combine the cream, milk, nutmeg, and salt. Stir frequently until the mixture reaches a gentle simmer.
Gradually add a large spoonful of the hot milk mixture to the egg yolk mixture, whisking vigorously each time. Repeat this process, adding one spoonful at a time, to temper the eggs.
Once most of the hot milk has been incorporated into the eggs, pour the mixture back into the saucepan.
Whisk constantly for about a minute, or until the mixture thickens slightly and reaches around 160 degrees Fahrenheit on a thermometer. It will continue to thicken as it cools.
Remove the saucepan from heat and stir in the vanilla extract.
Strain the eggnog through a fine-mesh sieve into a pitcher or container, then cover with plastic wrap.
Refrigerate until thoroughly chilled. For a thinner, completely smooth texture, blend the chilled mixture with one or two tablespoons of milk until smooth.
Serve topped with a sprinkle of cinnamon or nutmeg and, if desired, fresh whipped cream.
Store the homemade eggnog in the refrigerator for up to one week.