Rinse the Salt cod loins under cold water, then soak them in a bowl of cold water in the refrigerator for 24–48 hours to remove excess salt, changing the water every 6–8 hours; when ready, drain and pat the pieces dry and cut into large serving portions.
Thinly slice the Garlic cloves and gently crush or tear the Dried guindilla chiles to release their flavor.
Pour enough Extra-virgin olive oil into a deep skillet or shallow saucepan to come about halfway up the fish pieces (or almost cover them). Warm the oil over low heat until it shimmers but does not smoke.
Add the sliced garlic and the torn chiles to the warm oil and cook very gently until the garlic is pale golden and fragrant, about 2–4 minutes; remove the garlic and chiles with a slotted spoon and set aside (you can leave a few if you prefer a stronger flavor).
Place the drained cod pieces into the oil, skin side down if they have skin, and cook very slowly over low to medium-low heat. As the fish heats it will begin to release its gelatin—cook gently for about 6–10 minutes until the flesh is just cooked through.
To form the pil-pil sauce, either move the pan in small circular motions or use a wooden spoon to beat the oil against the sides of the pan while occasionally spooning the oil over the fish. Continue this motion until the oil and fish juices emulsify into a glossy, slightly thickened sauce (3–6 minutes); if the emulsion needs help, add a little more warm oil and continue.
Return some of the reserved garlic and chiles to the pan, baste the fish with the pil-pil sauce, check seasoning (no extra salt should be needed if the cod was properly desalted), and serve immediately with plenty of crusty bread to soak up the sauce.
