Add a big spoonful of the hot milk to the egg mixture, whisking vigorously. Repeat, adding a big spoonful at a time, to temper the eggs.
Once most of the hot milk has been added to the eggs, pour the mixture back into the saucepan on the stove. Whisk constantly for just a few minutes, until the mixture is just slightly thickened.
Pour the eggnog into a pitcher or other container and cover with plastic wrap.
Refrigerate until chilled. It will thicken as it cools. If you want a thinner, completely smooth consistency, you can add the entire mixture to a blender with 1 or 2 tablespoons of milk and blend until smooth.
Serve with a sprinkle of cinnamon, and fresh whipped cream. Add your favorite rum, brandy or bourbon upon serving if desired. Store in fridge.
Optional: rum, brandy, or bourbon, sprikle of cinnamon