Soak the salt cod in cold water in the refrigerator for 24–48 hours, depending on its thickness, changing the water at least twice. Drain, then place the fish in a saucepan and cover with fresh cold water. Heat just to boiling point, then remove the pan from the heat and leave to stand for 15 minutes.
Meanwhile, cook the potatoes in a separate saucepan of lightly salted boiling water for 15 minutes until tender. Drain well, then return to the pan and mash until smooth.
Drain the salt cod, discard any skin and bones, then flake into small pieces. Squeeze away any excess water from the shallot. Stir the salt cod, shallot, egg yolk and parsley into the mashed potato. Using your hands, form the mixture into about 16 small egg shapes and dust all over with flour.
Pour the oil into a large, deep saucepan or deep fat-fryer to a depth of at least 7 cm (3 inches) and heat to 180–190°C (350–375°F), or until a cube of bread browns in 30 seconds. Deep-fry the croquettes in 2 or 3 batches for about 3 minutes, until golden, then remove with a slotted spoon. Drain on kitchen paper and keep warm while you cook the remaining croquettes. Serve warm with lemon wedges for squeezing over.