Add cinnamon stick to mixture and allow to steep. This will enhance the egg nog slightly with some cinnamon flavor.
Stir mixture frequently and allow to thicken. You don't want to rush this process or you'll end up with scrambled egg nog. Cooking is finished when egg nog coats the back of the spoon.
When finished, remove saucepan from heat and allow egg nog to cool.
Remove cinnamon stick and refrigerate. Serve chilled by itself or with the option of an ounce or two of your favorite holiday spirit.
Notes
For a more traditional variation of this, you can substitute the coconut milk with heavy cream.
Recipe by Pastured Kitchen at https://www.pasturedkitchen.com/recipes/paleo-egg-nog/