Whisk egg yolks (just the yolks) and white and brown sugar together until well mixed. Set aside.
Pour milk, whipping cream, cinnamon, nutmeg, and salt into a pot and heat on medium low. Heat until just before boiling. Do not let boil.
When the milk mixture has heated up, take a few tablespoons of the milk mixture and mix it into the egg mixture while whisking vigorously. Add the rest of the milk mixture into the eggs cup by cup while you whisk it. You want to do this slowly to avoid cooking the eggs too fast and ending up with clumps. Do this until the milk mixture is completely mixed in with the eggs.
Pour the eggnog back into the pot and heat on medium high stirring constantly. Heat until just below boiling to thicken. Again, do not allow to boil.
Remove from heat and add the vanilla and rum extract.
Keep in fridge to cool until ready to serve.
