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1
Submerge the salt cod in cold water for a minimum of 48 hours, changing the water every 8 hours. The increased surface area of shredded cod accelerates migration of salt from the outer layers; the centre still requires the full period. Taste a strand: it should be pleasantly saline, not sharp. Remove, shred into thin strands by hand, and pat completely dry with paper towels — any retained moisture will produce steam in the pan, softening the potatoes and thinning the egg matrix.
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2
Cut the potatoes into fine matchsticks. Fry in batches in olive oil over high heat until rigid and golden. Drain on paper towels and hold uncovered at room temperature. They must remain dry and crisp until the final moment of assembly — this is their only purpose in the dish.
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3
Warm the olive oil in a wide, heavy pan over low heat. Add the sliced onions and garlic. Cook slowly, stirring occasionally, for a minimum of 30 minutes. The onions are ready when they are deep golden, completely soft, and visibly reduced to a fraction of their raw volume — pale or barely softened onions lack the sweetness required to balance the intensity of the salt cod.
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4
Raise the heat to medium. Add the shredded, dried cod to the caramelised onions and garlic. Toss to combine and warm through, 2–3 minutes. The mixture should be fragrant and the cod strands fully separated — no clumps, no pooling moisture in the pan.
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5
This is where the dish lives or dies. Remove the pan entirely from the heat. Pour in the beaten eggs and fold them continuously through the hot cod and onion mixture. The residual heat of the pan is sufficient — the eggs must be barely set, forming a light, custardy matrix that coats each strand of cod. Return the pan to the lowest possible heat for no more than a few seconds if the eggs appear entirely liquid, but remove again immediately. Rubbery, firm scrambled eggs cannot be corrected.
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6
Add the crisp batata palha immediately and fold once through the egg and cod mixture. Serve within seconds of combining — the straw potatoes begin to absorb moisture the moment they make contact. The finished dish should be moist and cohesive but not wet; the potatoes audibly crisp against the creamy egg.
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7
Transfer to a warmed serving dish or directly to plates. Scatter black olives and chopped flat-leaf parsley over the surface. Finish with a drizzle of extra-virgin olive oil and freshly ground black pepper. Serve at once.