Remove skins from the chicken breasts.
With a flat plate or platter, press the chicken as flat as possible.
Place 3 slices of ham on each breast.
Lay cheese on top, in the middle of ham.
Enfold the cheese: fold one side of chicken and ham over the cheese; fold in the ends; fold over other side.
Wrap tightly in plastic wrap; place in freezer until slightly frozen.
Meanwhile, crush saltines in a blender until very fine; pour into bottom of a flat dish.
Stir in the basil and fennel.
Combine egg, water, and vinegar in another flat bowl; beat to blend.
Remove chicken from plastic wrap and roll in egg mixture.
With your hand, remove any excess egg.
Roll chicken in cracker crumbs.
Wrap in plastic wrap and place in freezer until slightly frozen.
Heat oil to 365°F (184°C).
Remove plastic and fry chicken in deep oil until deep brown.