Combine the 6 whole eggs, 2 egg yolks, sugar, and salt in a medium mixing bowl and whisk together. Heat 2 cups heavy cream with the milk in a large saucepan over medium-low heat. When the cream and milk are hot, ladle about 1 cup into the egg mixture and whisk to incorporate. Pour the egg-milk mixture into the hot cream mixture, and continue to cook, stirring continuously, until the mixture thickens enough to coat the back of a spoon, 3 to 5 minutes. Remove the pan from the stove and strain the custard immediately through a fine-mesh sieve. Allow the custard to cool for 10 minutes before proceeding.

Add the vanilla, nutmeg, bourbon (if using), and brandy (if using) to the eggnog and stir well to incorporate. Beat the 2 egg whites to soft peaks in a clean mixing bowl and fold them into the custard base. In a separate bowl, beat the remaining 1/2 cup cream to soft peaks, and fold them into the eggnog as well. Cover and refrigerate until chilled, about 1 hour.

Pour into a decorative bowl or pitcher and garnish with nutmeg. Serve in small punch cups or old-fashioned glasses.