Place the salt cod in a rectangular glass Pyrex dish and cover it with cool water. Place it in the refrigerator, covered and allow it to soak in the water for 12 hours.
Drain off the salty water. Add more fresh cool water and return to the refrigerator.
Repeat this process for 3 days changing the water at least twice daily or until the salt cod is desalted to taste. By the end of the process, the cod should be plumped and only slightly salty. When the soaking process is finished, drain the cod and pat dry with paper towel.
If you are using reconstituted cod, skip the first three steps and just rinse and pat dry.
Remove any dark skin, tough flesh and bones from the fish.
Shred the cod with your fingers (or two forks) into small pieces around one inch (2.5 cm) in size. Shredding the cod produces the best texture. But depending on the size of the pieces of the cod purchased you may need to cut the cod into pieces first then shred it.
Place shredded cod in a glass bowl and toss lightly.
Finely dice onion. If it is strongly flavoured then first soak the diced onion in ice water for 15 minutes and drain.
Chop tomato, discarding the seeds and any liquid. Dice peppers into uniform pieces.
Fold onion, tomato and peppers into salted cod.
Add one half of the extra virgin olive oil and mix lightly. Mix only enough to coat the cod and vegetables with olive oil.
Squeeze fresh lemon juice over mixture and toss again. Adjust salt to taste.
Refrigerate covered for a minimum of 2 hours.
Turn out onto a platter (or individual tapas sized plates). Arrange black olives on top.
Drizzle with remaining olive oil.
Add freshly ground pepper to taste.
Serve and enjoy!