Rinse the salt of the cod.
Put in a medium pan and add enough cold water to cover the cod, then bring to a boil. After it begins to boil it will foam; skim off. Reduce heat to medium and cook for 15 minutes, then drain and rinse. Repeat 3 times.
Set aside to cool. When cool, shred the cod.
Boil the potatoes in salted water till fork tender. Drain well and mash. Cool completely.
Mix the potatoes, cod, eggs, onion, parsley, and pepper. Shape into 2 inch balls, then flatten into a patty to about 1 inch thick.
Put about 1/2 inch of oil in a skillet and heat over medium high heat.
Put some flour in a bowl and lightly coat each codfish cake. Fry in the oil on both sides until golden brown. Drain on paper towels.
Serve with mustard and saltine crackers.