Gently simmer the nut milk, heavy cream, cinnamon stick, and nutmeg in a medium saucepan for about 8–10 minutes, then move the pan off the burner. The liquid should smell warmly spiced and bubble gently rather than boil hard.
Beat the yolks and sweetener in a large bowl with a whisk or electric mixer. Look for a paler, fluffy mixture with most of the sweetener dissolved, allowing for remaining erythritol granules.
Whisk continuously as you introduce the hot spiced liquid to the yolks in a very thin stream. The bowl should warm gradually while the mixture stays smooth and free of cooked egg flecks.
Transfer the tempered mixture to the saucepan and stir over medium-low heat for roughly 8–10 minutes, aiming for 160°F/70°C and a coating on the back of a wooden spoon. The custard should gain body while remaining fluid, without reaching a rolling boil.
Take the saucepan off the heat and immediately pass the custard through a fine-mesh sieve into a medium mixing bowl. The sieve should catch the cinnamon stick and any egg specks, leaving a smooth liquid below.
Mix in the vanilla and your chosen liquor to taste, then cover the bowl and refrigerate to chill. The eggnog will become thicker as it cools.
Stir the chilled eggnog thoroughly before pouring, adding a little nut milk if needed. Stop thinning when it flows smoothly while retaining its creamy body.