1. In a saucepan, heat the milk over medium heat until it is hot but not boiling.
2. In a mixing bowl, whisk the egg yolks with ½ cup of sugar until the mixture is pale and thick.
3. Gradually add the hot milk to the egg yolk mixture, whisking constantly.
4. Pour the mixture back into the saucepan and cook over medium heat, stirring constantly, until it thickens slightly. Do not let it boil.
5. Remove from heat and stir in the heavy cream, rum, vanilla extract, and ground nutmeg. Let it cool.
6. In a separate bowl, beat the egg whites with the remaining ½ cup of sugar until soft peaks form.
7. Fold the beaten egg whites into the cooled eggnog mixture.
8. Chill the eggnog in the refrigerator for at least 1 hour before serving.
9. Serve the eggnog chilled, garnished with a sprinkle of ground nutmeg.