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1
Place the desalted shredded cod in a bowl. Pour over the hot milk — it must be steaming but not at a rolling boil. Leave to soak for 30–60 minutes. The cod is ready when it feels soft and yielding throughout and carries no sharp saline edge on the tongue.
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2
Warm the olive oil in a wide pan over a medium flame. Add the onion rings and cook gently, stirring occasionally, until soft and deep golden throughout — roughly 20–25 minutes. Do not rush this stage; the onion must be fully sweet and collapsed before it can carry the dish.
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3
Drain the cod from the milk. In an earthenware baking dish, build the layers in this order: a bed of golden onion, then shredded cod, then sliced potato; repeat — onion, cod, potato — finishing with potato on top. Each layer should be even.
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4
Pour olive oil over the entire surface with a generous hand. Every layer must be coated; the surface should glisten and a small pool of oil visible at the base of the dish. Under-oiling is the primary cause of a dry result.
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5
Bake uncovered at 200 °C for 25–30 minutes. The dish is done when the top layer of potato is tender to a skewer but still holding its shape, the edges are bubbling, and the kitchen carries a full savour of olive oil and salt cod — not a harsh, dry smell.
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6
Remove from the oven. Arrange the sliced or quartered hard-boiled eggs across the surface. Scatter the Portuguese black olives and the chopped parsley. Dust with pimentón if using. Bring the earthenware dish directly to the table.