1 (14 ounce) can sweetened condensed milk
1 cup rum, or more to taste (optional)
1 1/2 teaspoons vanilla extract
1/8 teaspoon aromatic bitters
1 pinch salt
1 pint orange sherbet
1 pinch ground nutmeg
Beat eggs in a large bowl with an electric mixer on high speed until thick and foamy, about 5 minutes. Stir in sweetened condensed milk, rum, vanilla extract, aromatic bitters, and salt. Freeze for 1 hour.
Pour egg mixture into a punch bowl. Add small scoops of orange sherbet; sprinkle nutmeg on top.