In a saucepan over low-medium heat, combine the milk, cream, vanilla, cinnamon, and nutmeg. Bring just to a gentle boil, then remove from heat and let it steep to infuse the flavors.
In a large bowl, beat the egg yolks and sugar until pale and thick. Gradually whisk in the hot milk mixture, about ½ cup at a time, to avoid scrambling the eggs. Once fully incorporated, stir in the rum.
Pour the mixture back into the saucepan and cook over medium heat, stirring constantly for 2 to 3 minutes until it thickens slightly. Remove from heat, let cool to room temperature, then refrigerate overnight or up to 3 days.
Before serving, beat egg whites until soft peaks form and gently fold into the chilled eggnog. Alternatively, top each glass with a dollop of whipped cream. Serve cold with a dusting of nutmeg or cinnamon.
