Heat butter in a non-stick skillet and saute chopped onion, celery and garlic until softened, about 3 minutes.
Combine in bowl with crab, egg, salt, pepper and cracker meal, and mix (dressing should stick together).
If too dry, add another egg. Stuff pepper halves liberally. Moisten stuffed peppers by dipping in cool water. Roll in more cracker meal to coat.
Deep fry (or fry in skillet) in hot vegetable oil until golden brown.
NOTE: To parboil, drop peppers into boiling water for a minute or two until semi-soft, then drain.