In a medium bowl, whisk together the egg yolks and sugar until light and creamy.
In a saucepan, bring the cream, milk, nutmeg and salt to a bare simmer, stirring often. Slowly ladle in 1/2 cup or so of the hot milk to the egg mixture, whisking vigorously to avoid little bits of cooked egg. This will temper the eggs so they don't scramble when cooked on the stovetop. Ladle in another 1/2 cup, whisking vigorously the entire time. Do this until all the hot milk has been added to the eggs and the mixture is well combined.
Pour the tempered egg mixture back into the saucepan of milk on the stove, whisking quickly, and cook the mixture, stirring constantly, until it reaches 160 degrees F on a thermometer.
Remove from the heat and stir in the vanilla and rum extract (if using).
Pour the eggnog into a bowl and cover with plastic wrap. Refrigerate until thoroughly chilled.
Milk: I use 1% milk when making this - you could probably get away with anything from skim to whole milk. Nutmeg: I happen to really love nutmeg - if you think the full 1 1/2 teaspoons might be a bit overwhelming, knock it down to 1 teaspoon to start and add more after tasting, if needed.