If using dry salt cod: Soak in water for 12 hours or overnight (in the refrigerator if the weather is warm), changing the water 4-6 times. Scrape off scales and remove visible bones, if any. If using frozen desalinated cod: Defrost and scrape off scales, if any. (Frozen steaks usually have no visible bones.)
Make the Skorthalia ahead of time. Peel the potatoes and boil in salted water until well done (easily pierced with a fork). Sprinkle with pepper and mash.
In the blender bowl of the food processor (or with a hand mixer), purée the potatoes and garlic until well mixed, about 30-45 seconds.
Still puréeing, slowly add the olive oil and vinegar, alternating between them until the mixture is smooth. Skorthalia should be creamy and thick.
If it gets too thick, add a little cold water (not more than 1/4 cup).
When ready to cook, cut the fish into 1 1/2 to 2 inch slices.
In a bowl, add the flour slowly to the water, stirring briskly with a wire whisk or fork until the flour has dissolved. The batter will be fairly thin.
Dip the fish into the batter and fry in hot oil, about 6-10 minutes per side (depending on the thickness) until dark golden.
Serve with one fourth of skorthalia garlic puree mixture per person.