Bacalao al pil-pil with emulsified sauce

Pat the desalted cod dry and check for bones. Keep the skin and cut pieces about 2.5 cm thick. Peel and slice the garlic and cut the chilli. Put the garlic, chilli and oil into a shallow casserole about 24 cm across, snug enough to hold the fish in one layer. Heat gently for about 5 min until the garlic is pale gold, then remove and reserve the garlic and chilli.

Take the casserole off the heat and let the oil fall to about 85 °C, allowing about 5 min. Add the fish skin side up. The oil partly surrounds it. Return to very low heat and maintain this temperature for about 15 min, regularly spooning oil over the top. Check a thick piece reaches 75 °C for 30 s at its centre, keeping the probe off the pan base. Continue if necessary. Lift the fish carefully onto a covered plate and keep all released juices.

Pour the oil and pan juices into a heatproof jug. Cool for about 10 min to approximately 45 °C. Let the layers separate, then gently ladle the clear oil from the top into a bowl, retaining the whitish juice at the bottom. Pour this juice into the casserole and add the juices from the fish plate. Keep all of this gelatinous liquid.

Off the heat, gently move the base of a small metal sieve in circles through the juices while adding the cooled oil in a very thin stream. Work slowly for about 8 min until the sauce is thickened and glossy. Incorporate each small addition before adding more. Return the fish, garlic and chilli to the sauce and warm over very low heat for about 2 min without boiling or breaking the emulsion. Serve immediately.