Soak the cod in cold water to cover in a cool spot or refrigerator for at least 24 hours or up to 3 days, changing the water frequently. After 24 hours, break off a tiny piece of fish and taste for saltiness. If fish is still quite salty, continue soaking until water is very clear and fish is almost sweet in taste.
Place potatoes in cold water to cover. Bring to a boil over high heat and cook for about 15 minutes or until potatoes are almost cooked through. Drain.
Heat oil in a large, heavy bottomed casserole over medium heat. Add the celery and saute for about 5 minutes, then add the onion and saute until vegetables begin to get soft. Add the olives and saute for an additional minute. Stir in the tomatoes and their juice. Bring to a boil. Lower heat and simmer for 10 minutes.
Stir in broth and return to simmer.
Stir in the potatoes and the soaked baccala and simmer for about 10 minutes or until the potatoes are cooked and the baccala flakes when poked with a fork.
Taste and, if necessary, add salt. Serve hot.
Often, salt cod dishes will require no additional salt. Therefore, always taste before adding any seasoning.