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.