Whisk the egg yolks and sugar together in a medium mixing bowl until light and fluffy.
In a saucepan over medium heat, stir together the cream, milk, vanilla extract, rum extract, nutmeg and salt until the mixture reaches a slight simmer.
Whisking vigorously, add a ¼ cup of the hot cream mixture to the egg mixture to temper the eggs. Then mix the egg mixture slowly into the cream mixture in the saucepan on the stove.
Whisk continuously for 3-4 minutes, until the mixture is thickened slightly (enough to coat a spoon) or until it reaches about 160°F/71°C. The mixture will thicken more as it cools.
Pour the eggnog into a large heat-resistant pitcher and cover with plastic wrap.
Refrigerate until chilled. It will thicken as it cools. If you want a thinner, smooth consistency, whisk the thickened mixture with 1 or 2 tablespoons of milk until smooth and reaches your desired consistency.
Store in the fridge for up to a week.
Serve with a sprinkle of cinnamon.
Notes
Bring the cream mixture to a slight, ever so gentle simmer – do not boil.
Once the egg mixture is added to the cream, whisk continuously until the mixture thickens to avoid scorching the mixture or sticking to the bottom of the pot.
Keep the heat to medium-low to avoid cooking the eggs too quickly. You want to cook them into the cream mixture slowly not scramble them.
Thickening enough to coat the spoon simply means when you dip a spoon into the mixture, it will cling to the spoon rather than run right off.
To add a festive look, garnish with star anise and a cinnamon stick too.
To serve a crowd feel free to double or triple the recipe.