In a medium heatproof bowl set over a medium pot of simmering water, whisk together the rum, ½ cup sugar, and the egg yolks and cook, whisking frequently, until very thick, 6–9 minutes. Remove from the heat, set aside to cool to room temperature, then transfer the custard to the fridge to chill.
Meanwhile, in a medium bowl, whip the cream until soft peaks form. Transfer to the fridge to chill.
In the bowl of a stand mixer fitted with the whip attachment, whip the egg whites, remaining sugar, cinnamon, allspice, anise, and nutmeg, until soft peaks form. Using a silicone spatula, fold the whipped cream and cooled egg yolk mixture into the whites, then stir in the milk. To serve, ladle the eggnog into mugs or small glasses and garnish with ground cinnamon and nutmeg. Serve with additional rum on the side, if you like.
Fold whipped cream and cooled egg yolk mixture into whites; stir in milk. To serve, ladle eggnog into mugs and garnish with ground cinnamon and nutmeg. Serve additional rum on the side, if you like.