In a large, heavy-bottomed saucepan, beat together the eggs and sugar. Stir in the half-and-half. Cook over medium-low heat, stirring constantly, until the mixture is thick enough to coat a metal spoon with a thin film and reaches at least 160 degrees F. Remove from the heat. Stir in the cream, nutmeg, vanilla, bourbon, and brandy. Cool, then cover and refrigerate until ready to serve.

Just before serving, beat the egg whites in a large bowl with an electric mixer on high speed until stiff peaks form, then fold them into the eggnog. Serve cold in punch cups and sprinkle with nutmeg.