Make sure to use skin-on salt cod; the natural gelatin in the skin is vital to emulsifying the sauce. Put four 4" × 4" skin-on boneless salt cod filets (about 1 1⁄2 lbs.) into a large bowl. Cover cod with water, refrigerate, and soak, changing water 6–8 times, for 48–72 hours. Remove cod from water; pat dry. Heat 1 cup extra-virgin olive oil in a large skillet over medium-low heat. Add 5 thinly sliced cloves garlic; cook, stirring, until garlic is light golden brown, 4–5 minutes. Using a slotted spoon, transfer garlic to a plate; set aside. Reduce heat under skillet to very low; let cool for 5 minutes. Add cod filets, skin side up, and cook until just hot, spooning the hot oil over them, 8–10 minutes. Carefully transfer all but a few tablespoons of the oil to a small pot over very low heat. Flip cod filets; arrange toward center of skillet. Allow cod to cook gently until bubbles of gelatin begin to form in oil. Gently rock skillet back and forth every 1–2 minutes while whisking oil in skillet constantly to form an emulsion. As more gelatin forms in skillet, slowly drizzle in reserved oil a few tablespoons at a time, while whisking constantly, to make a smooth sauce, about 20 minutes in all. Garnish with reserved garlic. Serves 4.