Separate the eggs and place each in large bowls. Set the egg whites aside.
In a large saucepan, combine the milk, cream and nutmeg. Bring to a boil over medium-high heat.
While the cream is coming to a boil, beat the egg yolks until light in color.
Add the 1/3 cup of sugar to the beaten yolks and beat for 3 minutes.
Once cream comes to a boil remove it from heat. Slowly drizzle the egg yolk mixture into the hot cream whisking constantly. Adding the eggs slowly and whisking briskly will keep the eggs from scrambling like they would if you added them all at once! This is called "tempering the eggs". Continue slowly drizzling and whisking until completely combined.
Pour the mixture back into the saucepan and return to heat.
Cook through until you reach an internal temperature of 165F.
Remove the eggnog mixture to the fridge. (I placed back in the bowl and left uncovered.)
While the eggnog is cooling, beat the egg whites with 1 Tablespoon sugar until soft peaks form, about 4-6 minutes.
When the eggnog mixture is well chilled, whisk in the egg whites.
To ensure even distribution of the rum, I prefer to add 1 oz to each mug and give a decent stir.
Serve warm or cold.
For those concerned about raw eggs, this is a cooked eggnog. The yolks and cream are cooked through, but the whites are incorporated while fluffy and cold. You could potentially leave out the whites but the texture will be thicker and the taste will be less balanced with a stronger egg taste.
Using pasteurized eggs and ensuring that the egg whites don't come into contact with the outer shell are your best bets to prevent any issues with the raw egg whites.