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, and brandy 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 it into the eggnog as well. Serve warm or 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.