Beat egg yolks and ½ cup sugar using an electric mixer on medium-high speed until very pale yellow, about 5 minutes. Transfer to a punch bowl or large pitcher. Fold in half-and-half, whiskey and rum.

Beat egg whites to soft peaks. Gradually add remaining ¼ cup sugar and continue beating until stiff peaks form. Gently fold into egg yolk mixture.

Ladle into cups and dust with nutmeg, if desired.