Just cover the fish in cold water, and bring to a low simmer. Cook 5-10 minutes, until fish flakes easily. Remove from liquid with a slotted spoon, reserving stock, and place in bowl to cool.
Scrub potatoes, and cut in roughly 1-2" pieces. Boil in reserved liquid from cooking fish until tender. Drain and mash. Stir in parsley and salt.
Flake fish into small pieces (checking for any bones that may have been missed in the filleting process. Stir fish into mashed and seasoned potatoes. Form into cakes.
Heat oil in pan. Add fishcakes to pan, and cook until brown on one side, then flip, and brown the other side. Repeat with remaining fishcakes.
Notes
Serve with tartar sauce, to be traditional, or other condiments of choice.