Stir together egg and sugar in a large saucepan; gradually stir in milk. Cook over medium heat, stirring constantly, 18 to 20 minutes or until mixture thickens and coats a metal spoon. Remove from heat; stir in brandy, rum, and vanilla. Cover and chill 8 hours.
Beat whipping cream at high speed with an electric mixer until soft peaks form; fold into chilled egg mixture. Garnish, if desired.
Very rich, very sweet as is. I would heat it at the lower end of the medium spectrum and probably use half the sugar. The first time I cooked it at too high a setting, and it ended up like custard. I might try a little less vanilla next time, too.
This is so good! The best egg nog I've ever had. Very rich - you can only drink a small amount. I made it without the alcohol, and added an extra cup of milk. I also added ground nutmeg to the eggnog, instead of just sprinkling it on top. yum.