In a large bowl, beat together the egg yolks and 1/2 cup of sugar until they turn light in color. Stir in the milk and heavy cream. Slowly whisk in both rums. Set aside for 20 minutes to allow the alcohol to “cook” the yolks.
In a separate bowl, beat the egg whites with the remaining 1/4 cup of sugar until they form soft peaks. Fold the egg whites into the yolk mixture.
Serve topped with freshly grated nutmeg in punch or teacups.