Make-Ahead: Eggnog should be chilled at least 4 hours before serving, and served within 24 hours.
This has an even creamier texture than the old-fashioned kind made with heavy cream. The cooked egg yolks make this the nog of choice for cooks who prefer to avoid raw eggs.
1. In a medium saucepan over medium heat, stir the half-and-half with the sugar until the sugar dissolves and the mixture is hot. In a medium bowl, whisk the egg yolks. Gradually whisk in the hot mixture. Return to the saucepan and cook over low heat, stirring constantly, until the mixture is thick enough to coat a spoon (a thermometer will read about 185° F.), about 3 minutes. Strain into another medium bowl. Cool completely. Whisk in the rum, brandy, and bourbon. Cover and refrigerate until well-chilled, at least 4 hours.
2. In a chilled, medium bowl, beat the heavy cream just until stiff. Fold into the chilled custard. Pour into punch bowl and add the ice cream. Grate the nutmeg over the eggnog, and serve chilled.