Add egg whites to a blender and turn on the lowest setting until the egg whites form stiff peaks, checking frequently to make sure the egg whites are not getting warm.
Once the egg whites form stiff peaks, add the remaining batter ingredients and blend until the batter is smooth.
To serve:
Add 2 oz of batter and the brandy/bourbon and rum to a mug.
Top with hot milk and stir until combined.
Grate fresh nutmeg over the top of each cocktail to serve.