Combine milk and 1/4 c. sugar in a medium saucepan. Heat over medium heat, stirring to dissolve sugar until a rim of fine bubbles appears around edge of pan.
Beat egg yolks until thick and lemon-colored. Add a small amount of hot milk and egg yolks: return all to saucepan.
Cook over medium heat for 5 minutes, stirring constantly. Pour into a bowl. Add ice cream by spoonfuls, stirring until melted.
Add brandy and vanilla extracts. Cover and refrigerate.
Refrigerate unbeaten egg whites, covered in separate containers.
Just before filling punch bowl., let egg whites stand at room temperature in large bowl of mixture for 15 minutes.
Beat whites until foamy. Add salt and continue beating until soft peaks form. Add 1/4 c. sugar, 1 tbsp. at a time, beating constantly.
Continue beating until sugar is dissolved and whites are glossy and again stand in soft peaks.
Fold custard mixture into whites, using a large whisk.
Pour eggnog into chilled punch bowl. Ladle into punch cups and sprinkle with nutmeg.