For the batter: Whisk egg whites until stiff peak, then hold aside.
Combine remaining aged alcohol, vanilla, powdered sugar, apple pie spice and nutmeg with a paddle attachment and mix until mix has increased in volume by 50%, about 4-5 minutes.
Fold egg whites and egg yolk mixture until combined. (Can refrigerate batter for up to a week.)
For the cocktail: combine hot water, hot milk, aged rum, brandy, 2 oz. of batter and nutmeg in a mug.
Stir to combine.
Garnish with grated nutmeg.