Beat the egg whites until soft peaks form. Add 6 tablespoons of the sugar, one spoon at a time, beating until stiff, but not dry. Transfer to a gallon container or punch bowl. Beat the egg yolks and ¾ cup sugar in a large bowl until pale yellow and a slowly dissolving ribbon forms when the beater is lifted. Fold gently into the egg whites. Beat the whipping cream until soft peaks form. Add to the egg mixture and fold together gently. Gently stir in the milk, then gently stir in the bourbon and rum. Cover and refrigerate overnight. Just before serving, gently fold together to recombine. Top with freshly grated nutmeg.