In medium bowl, beat together eggs, sugar and salt. In medium saucepan, heat 2 cups milk over medium-low heat just until hot. Slowly whisk milk into egg mixture. Return egg-milk mixture to saucepan. Cook mixture over low heat, stirring constantly - about 15 to 20 minutes or until slightly thickened (thermometer should register 160 degrees F). Remove from heat. Stir in remaining milk and vanilla.
Transfer to a clean bowl; cover and refrigerate until thoroughly chilled - several hours or overnight.
Just before serving, beat whipping cream until soft peaks form. Transfer eggnog to punch bowl. With wire whisk, stir in rum, then fold in whipped cream. Garnish with grated nutmeg. Makes 12 servings.