Rinse cod under cold water. Place pieces in large bowl; submerge completely in cold water. Cover bowl with plastic wrap; transfer to refrigerator. Let soak 24-36 hours, changing water every 8 hours. Rinse cod and discard soaking water; transfer to medium saucepan filled with water. Place saucepan over medium-high heat. Bring water to boil. Reduce heat to low. Simmer, skimming off foam that rises to surface, until cod is tender, about 10 minutes. Drain cod. When cool enough to handle, tear into bite-sized pieces; set aside.
Meanwhile, heat olive oil in large non-stick skillet over medium heat. Add onions. Cook, stirring occasionally, until slightly softened but not browned, about 8 minutes. Add garlic, cook until fragrant, about 30 seconds; remove skillet from heat and let olive oil mixture cool in pan.
Add red wine vinegar to pan with cooled olive oil mixture; stir to combine. Transfer cod to pan. Stir gently until completely coated in olive oil mixture; refrigerate until chilled.
Spoon cod mixture onto large serving platter. Decorate platter with tomato wedges, egg slices, avocado slices, olive halves and cilantro. Drizzle with more olive oil, if desired. Serve cold with hot, cooked tropical vegetables.
Soaking salted cod is a necessary step in ridding the salt used for preservation. After 24 hours of soaking, remove a small flake of flesh and taste. The meat should be firm, fresh and flavorful (not salty). If needed, continue to soak the cod in new water. Otherwise, use immediately.