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1
Taste the desalted cod before proceeding. It should be pleasantly saline but not sharp on the tongue. If still too salty, return to fresh cold water and change it again after 8 hours. The dish cannot recover from oversalted fish at any later stage.
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2
Dry the cod portions thoroughly with a cloth. Place them skin-side down in the cazuela. Add the room-temperature olive oil and sliced garlic. Set over the lowest possible flame and bring the oil slowly to 60–70 °C. Hold this temperature throughout: the oil should barely shimmer and produce no sound. The cod is ready to turn when the flesh has turned opaque two-thirds of the way up the sides and the skin releases cleanly from the earthenware.
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3
Lift the cod from the cazuela and set aside on a warm plate. Remove the garlic slices and reserve. Pour off the oil into a separate vessel and allow both the oil and the milky cooking juices remaining in the cazuela to cool until the oil is barely warm to the touch — no more than 50 °C. This step is where the dish lives or dies: oil that is too hot when the emulsification begins will fracture the developing sauce and no subsequent agitation will restore it.
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4
Begin reintroducing the reserved oil into the cazuela in a thin, slow stream, swirling the cazuela continuously in a steady circular motion. Add the cooking juices and oil alternately, a small measure at a time, never stopping the circular motion. The sauce is forming correctly when it turns opaque white, thickens visibly, and begins to coat the sides of the cazuela with each rotation.
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5
Return the cod portions to the cazuela, skin-side up, along with the reserved garlic slices. Continue swirling gently over the lowest heat for two to three minutes to marry the fish with the sauce. The finished sauce should be opaque white, trembling when the cazuela is nudged, and flow slowly — it coats the back of a spoon and does not separate when the motion stops.