In a large bowl, combine egg yolks, 2 cups sugar and rum. Mix well, cover and refrigerate for 24 hours.
Stir half-and-half into cooled yolk mixture. In a large bowl, whip the heavy cream until soft peaks form; set aside.
In a separate clean bowl, with a clean whisk, whip egg whites until thick, then gradually add sugar and whip until peaks form. Fold the whipped cream into the egg whites, then fold into the yolks mixture. Sprinkle top with nutmeg.