Pour the milk and cream into a medium size saucepan and heat over medium heat.
Add in the ground nutmeg and salt. Stir to combine. Bring this mixture to a simmer.
Meanwhile, add the egg yolks to a medium sized bowl. Mix together with a hand mixer or whisk.
Mix in the sugar and continue to beat on for 2-3 minutes until egg mixture is thick and you can see ribbons as it mixes.
Once milk mixture is simmering, temper the eggs by ladling 2-3 spoonfuls of hot milk into the eggs while mixing continuously. Continue until egg mixture is pourable.
Pour the egg mix into the saucepan with the rest of the milk while whisking.
Continue whisking until the eggnog reaches a temperature of 160 degrees F. Check the temperature, as this can happen immediately.
Remove the pan from the heat and stir in the vanilla and rum extracts.
Pour eggnog through a fine mesh sieve into a pitcher and chill in the refrigerator for at least 4-6 hours before serving.
After chilling, whisk together the eggnog before serving.
If eggnog is too thick, you can add milk to thin it out to desired consistency.
Top with whipped cream when serving if desired.