Beat egg yolks until light in color. Gradually add the 1 3/4 cups sugar, beating constantly. Add vanilla and nutmeg; beat well. Place in punch bowl; add rum gradually, stirring constantly. Add brandy, continue to stir until well blended. Let mixture stand in refrigerator or cold place overnight (yes you lose some of the alcohol - we're going for taste here not a buzz). Stir occasionally.

Before serving, add milk and cream a small amount at a time. Beat egg whites with the 6 tablespoons sugar. Fold into eggnog mixture. Sprinkle all, or, each serving with nutmeg.