Let's take a moment to talk about your options here first. If you don't want the eggs in your eggnog, simply omit them. But you will have to reduce the milk by about half to get it to thicken properly.
Place all ingredients in a blender and blend for about 2-3 minutes ( I used the pot I was going to cook it in and my hand blender).
Pour the eggnog into a pot and warm over medium-low heat for 15 minutes to cook the egg. You want this to get hot, but you do NOT want to boil it. Towards the end, it will want to simmer. Whisk constantly to avoid it.
Remove from heat and set the pot in the fridge when it's cooled enough to do so. Chill overnight.
If you made this with the exact listed ingredients (no substitutions), you will see that when it's cold, it becomes very thick. Blend with a whisk.
If you find that it's far too thick, simply add a bit more milk until you reach the consistency you enjoy.
Pour into cups and sprinkle with cinnamon.
Please note that the nutrition data below is a ballpark figure. Exact data is not possible.