In a large bowl, beat together the egg yolk mixture and sugar with a stand mixer or electric whisk until pale and creamy (about 2–3 mins).
In a medium saucepan, combine the whole milk, heavy cream, and warm spices. Cook over medium heat until steaming, but do not boil.
Temper the eggs by slowly drizzling (with a ladle) about half of the hot milk into the egg mixture while whisking constantly. This prevents the eggs from scrambling.
Return everything to the saucepan and cook on medium heat, stirring constantly with a wooden spoon, until it coats the back of a spoon or reaches about 160°F on a thermometer. (Do not let the mixture boil, as this will cause it to curdle.)
Remove from heat and then strain through a sieve or a mesh strainer into a medium bowl. Finally, stir in the vanilla. (I like to stir in the vanilla after the eggnog has cooled slightly—this keeps the flavor fresh and prevents it from cooking off.)
Pour into a large jug or airtight container and refrigerate for at least 2 hours before serving. To chill faster, place jar into an ice bath.