1. Separate the eggs.
2. Set aside the egg whites in a container in the refrigerator.
3. In a large mixing bowl, beat the egg yolks, sugar, rum, cognac, milk, and cream until smooth.
4. Chill in refrigerator overnight.
5. When ready to serve, put the refrigerated rum mixture into a punch bowl.
6. Beat the egg whites until stiff and fold them into the refrigerated rum mixture.
7. Sprinkle nutmeg on top.