Total time: 2 hours, 30 minutes
In a heavy saucepan, whisk together eggs and sugar until well blended; whisk in milk. Cook over medium heat, stirring constantly with a wooden spoon, until mixture thickens and reaches 140° on a candy thermometer, about 5 minutes.
Strain into a bowl; stir in nutmeg and vanilla. Cover and refrigerate until chilled.
When ready to serve, fold in whipped cream. Serve in a punch bowl, sprinkled with nutmeg, and with alcohol on the side; each 1/2 cup serving of eggnog gets about 1/2 ounce alcohol, as desired.