Whisk the egg yolks and sugar together in a medium bowl until light and fluffy.
In a saucepan over medium-low heat, combine the milk, cream, nutmeg, cloves, and salt. Stir often until mixture reaches a bare simmer.
Whisk ½ cup of the hot milk mixture slowly into the egg mixture to temper the eggs. Continue slowly adding the milk until incorporated.
Transfer the mixture back to the saucepan and return to the stove.
Increase temperature to medium heat, whisking constantly for 3-4 minutes, until the mixture is just slightly thickened. Do not allow it to boil.
Remove from heat and stir in the vanilla and rum. Remove and discard the cloves, and allow the eggnog to cool for 1 hour before transferring it to a pitcher.
Refrigerate overnight before serving for best taste. Store in the fridge for up to one week.
*Nutritional information is an estimate. Please consult a doctor or nutritionist for the most accurate nutritional info.