Cook the eggnog for about 8-10 minutes until it starts to thicken and slowly cook the eggs. It will be frothy at first. (We want the mixture to get hot, but not to simmer or boil. If it gets close to boiling, you can temporarily remove from the heat.)
Strain the mixture using a fine mesh strainer to remove the cloves and any other bits. You can stir in the optional vanilla extract at this time.
Pour the strained mixture into a 9x5 loaf pan, and freeze until thick and creamy, like soft-serve ice cream, about 6-8 hours.