Peel, wash, and slice the potatoes but not too thinly. Cook in a large pan covered with salted water together with the onion, parsley, and oil for ten minutes.
Wash and drain the slices of hake. Season and add carefully to the pot of potatoes just before they are completely cooked. When the mixture comes to a boil again, cover the pan, remove from the heat and leave to stand for ten minutes.
Sauce: Heat the oil in a frying pan, fry the sliced garlic cloves and remove when brown. Add the paprika to the oil taking care not to burn it, then remove the pan from the heat and add the vinegar and a little salt. Leave to stand, then pour off the red oil leaving behind any paprika dregs. Remove the slices of hake from the stock and serve. Place potatoes alongside the fish and pour the sauce over both. Half a ladle of the fish stock may be added to the stock if wished. Serve immediately.
This sauce can be used for cauliflower, cabbage, or any cooked fish. The secret of this dish is that the hake should be cut in thick slices and not over-cooked, so that it remains moist.