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1
Warm the olive oil in a wide pan over a medium flame. Add the sliced onions and cook, stirring occasionally, until completely soft and pale gold — they must not colour deeply. The test: a piece pressed between finger and thumb offers no resistance.
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2
Make the béchamel densa. Melt the butter in a heavy saucepan, add the flour, and stir constantly over a medium heat for 2 minutes. Add the warmed milk in a steady stream, whisking without pause, then pour in the cream. Continue to cook, stirring, until the sauce is thick enough to hold a clear channel when a spoon is drawn across the base of the pan. Season conservatively — the bacalhau carries residual salt. Grate in the nutmeg. If using, remove the pan from the heat and stir in the egg yolks before they can scramble.
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3
Fry the sliced potatoes in olive oil until cooked through and lightly golden at the edges. Drain on a rack. The test: a slice bends without breaking but does not crumble.
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4
In a large bowl, combine the shredded bacalhau, softened onion, fried potato slices, and roughly two-thirds of the béchamel. Fold together so that every element is evenly coated. Transfer the mixture to an earthenware gratin dish. Spread the remaining béchamel in an even layer over the surface.
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5
Bake at 220 °C for 20–25 minutes. This is where the dish lives or dies: the surface must achieve a deep, uneven golden-brown, with darker spots where the cream has caramelised at the edges. A pale or uniformly cream surface means the heat was insufficient or the time too short. The smell shifts from milky to toasted and savoury; the dish bubbles at the rim.