In the bowl of a stand mixer, beat the egg yolks until they lighten in color. Gradually add the 1/3 cup sugar and continue to beat until it is completely dissolved. Set aside.
In a medium saucepan, over high heat, combine the milk, heavy cream and nutmeg and bring just to a boil, stirring occasionally. Remove from the heat and gradually temper the hot mixture into the egg and sugar mixture. Then return everything to the pot and cook until the mixture reaches 160 degrees F. Remove from the heat, stir in the bourbon, pour into a medium mixing bowl, and set in the refrigerator to chill.
In a medium mixing bowl, beat the egg whites to soft peaks. With the mixer running gradually add the 1 tablespoon of sugar and beat until stiff peaks form. Whisk the egg whites into the chilled mixture.