Soak the Salted Cod in cold water for about 24 hours, changing the water 2–3 times to remove excess salt (shorter or longer depending on how salty your cod is).
Drain the cod, place it in a pot with fresh cold water and a Bay Leaf, bring to a gentle simmer and cook 10–15 minutes until the fish flakes easily; drain, let cool slightly and flake the fish, removing any skin and bones.
Thinly slice the Onion and finely chop the Garlic.
Heat a generous splash of Olive Oil in a large skillet over medium heat, add the sliced onion and cook until soft and lightly golden, then add the garlic and cook for another minute until fragrant.
Add the flaked cod to the skillet and sauté briefly to combine and warm through, breaking up any large pieces; taste before salting since the cod may still be salty.
Stir in most of the Batata Palha (reserve a handful for garnish) so the mixture gains some crisp texture.
Beat the Eggs lightly in a bowl with a small pinch of Salt and freshly ground Black Pepper, then pour the eggs over the cod mixture off the heat or over the lowest flame and stir gently until the eggs are just creamy and set — avoid overcooking.
Fold in chopped Flat-Leaf Parsley, scatter the Black Olives and remaining batata palha on top for crunch and color, adjust seasoning to taste, and remove from heat.
Serve immediately while warm and creamy, with extra parsley or a lemon wedge if desired.
