How to Make It
In a large skillet, warm 1/3 inch of oil over moderate heat. Add the potatoes, onion and a generous pinch of salt and cook, stirring occasionally, until browned, about 20 minutes. Using a slotted spoon, transfer the potatoes and onion to 4 bowls; keep warm.
Strain the oil through a fine sieve into a heatproof bowl, then return it to the skillet. Add the garlic and cook over moderately low heat until golden, 5 minutes. Discard the garlic. Add the cod to the skillet and cook, turning once, until just white throughout, 7 minutes. Using a slotted spoon, add the cod to the potatoes.
Pour off all but 1/3 cup of the oil from the skillet and let cool slightly. Stir in the 1/4 cup of oil and the water and bring to a simmer over moderate heat. Stir in the parsley and season with salt. Spoon the salsa verde over the fish and potatoes and serve.