Prepare an ice-water bath. In a medium saucepan, scald 2 cups milk. Meanwhile, with an electric mixer on medium-high, whisk 5 large egg yolks and 3/4 cup sugar until very thick and pale yellow, 3 to 5 minutes.
Add half the scalded milk to the yolk mixture, and whisk until blended. Stir into remaining milk, and cook, stirring constantly, over low heat until it is thick enough to coat the back of a spoon. Remove from heat, and immediately stir in 1 cup heavy cream. Pass the mixture through a sieve into a medium mixing bowl set in the ice-water bath. Let stand, stirring from time to time, until chilled.
Stir in another 1 1/2 cups milk and 1 cup dark rum. Transfer eggnog to a punch bowl or to individual glasses. Whip 1 cup heavy cream to soft peaks. Top each serving of eggnog with a dollop of whipped cream, and sprinkle with grated nutmeg.