Immerse salt cod in cold water; let sit in refrigerator 1 to 2 days, rinsing frequently (in testing, we found that a 24-hour soak was adequate if the water was changed four times). In a stockpot, cover potatoes with water and bring to a boil, then add fish. Simmer 10 to 12 minutes, until potatoes are not quite fully cooked. Separate cod and potatoes; set aside.

Preheat oven to 350 degrees. In a large skillet, sauti¿½ onions and garlic in 2 tablespoons olive oil until browned. Add ½ cup parsley and cook until soft. Remove from skillet and set aside. Next, add another 2 tablespoons olive oil to the skillet and brown potatoes (you may need to do this in batches). Lay the browned potatoes in the bottom of a covered casserole dish. Break cod into small chunks, removing any skin, and place on top of potatoes. Spread the onion, garlic, and parsley mixture over the cod. Top with chickpeas, then olives. Pour 1 cup olive oil over casserole. Bake, covered, 30 to 35 minutes, until the olive oil simmers. Remove pan and spread sliced eggs on top. Sprinkle lightly with salt and pepper and bake 10 minutes longer. Garnish with remaining ½ cup parsley and serve.