12 eggs, separated
1 (16 ounce) package confectioners’ sugar
1 cup dark rum
1 cup peach brandy
2 cups peach-flavored bourbon liqueur (such as Southern Comfort ®)
2 quarts heavy whipping cream
1 pinch ground nutmeg, or more to taste
Beat egg yolks in a bowl until thickened and light in color. Gradually beat in confectioners' sugar until smooth. Drizzle dark rum and brandy into egg yolk mixture, stirring constantly, until fully incorporated. Cover and let mixture stand for 1 hour to reduce the 'eggy' flavor.
Whisk bourbon and cream into the egg yolk mixture, stirring constantly, until fully incorporated. Cover and refrigerate for flavors to blend, 3 to 5 hours.
Beat egg whites in a bowl until foamy. Continue to beat until stiff peaks form. Lift your beater or whisk straight up: the egg whites will form sharp peaks. Fold egg whites into egg yolk mixture. Pour eggnog into a punch bowl and sprinkle with nutmeg.