Boil the potatoes (preferably in their skins, so the potatoes don't absorb water). Peel the potatoes and mash or sieve them. Set aside.
Meantime, simmer the previous soaked cod in enough boiling water to cover until tender, about 20 minutes. Drain the cod, discard the skin and bones, and flake the fish as much as you can with your fingers or a fork to reduce it to threads.☞ TESTER TIP: The proper way of doing this is to place the flaked cod inside a clean cloth, fold it and squeeze and pound the contents of the cloth with your fists. In this way you will have mashed cod.
Mix the cod with the mashed potatoes and add the eggs, 1 by 1, and then the onion and parsley. Taste and, if desired, season with salt. You may not need to add any, as the cod itself retains quite a lot of saltiness, in spite of being soaked and boiled. The mixture should be quite stiff, enabling a spoon to stand up in it. If you find it excessively dry, add one or two tablespoons of milk. ☞ TESTER TIP: Allow this to cool completely before frying.
With two tablespoons, shape the mixture into quenelles--egg-shaped ovals. Don't feel like spoon shaping? You can roll the mixture into 1 ½-inch balls.
Heat 4 or 5 inches of oil in a medium saucepan to (370°F/190°C). Carefully lower each pasteis into the oil with a spoon. Turn them three or four times to get nicely browned all over.
When cooked, lift them with a big fork or slotted spoon and place them on kitchen paper to absorb excess fat. Continue molding and frying until you use up the mixture.