In the bowl of a stand mixer, beat together the egg yolks and 1/3 cup sugar until the yolks lighten in color and the sugar is completely dissolved. Add the milk, cream, bourbon, rum, and nutmeg and stir to combine. Move mixture to a medium mixing bowl and set aside.
Place the egg whites in the bowl of the stand mixer and beat to soft peaks. With the mixer still running, gradually add the remaining 1 tablespoon of sugar and beat until stiff peaks form. Gently fold the egg whites into the mixture. Chill and serve.