Drain the canned salmon, reserving two tablespoons of the liquid. Remove any skin and bones, if wished, then break the salmon into chunks.
Cook two of the eggs in simmering water for 12 minutes to hard-boil them. Cool in cold water, then shell and chop them.
At the same time, cook the potatoes in lightly salted boiling water until tender, about 20 minutes. Drain thoroughly and mash them, adding the reserved salmon liquid. Mix in the salmon chunks, hard-boiled eggs, peas and parsley. Season with salt and pepper, then form the mixture into eight fish cakes.
Beat the remaining egg in a shallow bowl. Sprinkle the flour and breadcrumbs onto separate plates. Dust the fish cakes with flour, dip them into the beaten egg, then coat in breadcrumbs. Chill for ten minutes.
Heat the vegetable oil in a frying pan and shallow fry the fish cakes for about three to four minutes on each side. Drain on kitchen paper, then serve.
Cook's Tip: This is a brilliant recipe for using up leftover mashed potatoes, so next time you are making mash make plenty so that you have enough for these fish cakes.