Whisk 6 large egg yolks, 1 cup (200 g) sugar, and a pinch of kosher salt in a large punch bowl just until sugar is dissolved.
Whisk in 3 cups whole milk, 2 cups dark rum, and 2 cups heavy cream.
Cover and chill eggnog base at least 2 hours.
Just before serving, using an electric mixer, beat 6 large egg whites in a medium bowl until stiff peaks form.
Gently fold into eggnog base.
Finely grate whole nutmeg and cinnamon stick over as desired.
