Soak the salted cod fillets in cold water for 24 hours, changing the water several times to remove excess salt.
Peel the potatoes, slice them thinly or dice them, and fry in hot oil until golden brown. Drain on paper towels and set aside.
In a large skillet, heat the olive oil and sauté the thinly sliced onions and minced garlic until translucent.
Add the cod to the skillet and simmer for 5-10 minutes, or until the fish is tender. Remove any bones and skin, then shred the fish into small pieces.
In a separate saucepan, prepare a béchamel sauce: heat the milk and cream, then whisk in the flour. Continue stirring constantly until the sauce thickens. Season with salt and pepper to taste.
Place the fried potatoes in the bottom of a baking dish, top with the cod and onion mixture, then pour the béchamel sauce over the top. Sprinkle with grated cheese.
Bake in a preheated oven at 350°F (180°C) for 25-30 minutes, or until the top is golden brown and bubbly.
Before serving, sprinkle with fresh, chopped parsley and serve warm.
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