If your cod isn't pre-desalted, soak it in cold water for 48 hours, changing the water every 8 hours. Once desalted, pat the fillets dry with kitchen paper.
Pour 500 ml of extra virgin olive oil into a heavy-based frying pan or cazuela and heat it over the lowest possible setting (about 60-70 °C if you have a cooking thermometer). Gently confit the cod fillets skin-side up for 8-10 minutes until they release their gelatin. Remove and keep warm.
Increase the heat to medium-low and add the sliced garlic cloves and dried chillies. Fry gently for 2-3 minutes until fragrant and lightly coloured, taking care not to burn them. Remove and set aside.
Allow the oil to cool for about 5 minutes. Off the heat (or over the lowest setting), gradually add the gelatin-rich juices released by the cod. Using a fine sieve or a whisk, stir continuously in a circular motion until the sauce emulsifies and becomes creamy. If it splits, whisk in 1 teaspoon of cold water and continue whisking.
Return the cod fillets to the pan, skin-side down, and warm through for 2 minutes, tilting the pan so the sauce coats the fish.
Serve immediately, scattered with the reserved garlic and chillies, and with crusty bread for dipping.