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Boil the potatoes in salted water until tender. Drain.
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Bring the wine, shallots, garlic, thyme, and pepper to a boil in a large saucepan. Add the cod, cover and steam for 5 minutes or until thoroughly cooked.
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Remove the fish and drain on paper towel. Discard the cooking liquid.
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Place the hot potatoes and fish in a bowl and break them up with a fork until well mixed. Add 1 tbsp of olive oil. Add the butter, 1 tbsp of salt, and parsley, mixing after each addition. Chill 1 hour.
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Put a 14 inch piece of plastic wrap on a wet counter. Place the cod mixture on the plastic at one end and form into a log. Roll the log in the plastic and twist to seal. Place in the freezer several hours or up to two weeks.
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Preheat the oven to 250 F.
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Cut six slices from the cod log and thaw for 15 minutes. Heat ¼ inch of oil in a skillet over medium heat. Dip the cakes in flour and then sauté for 2 minutes on each side. Keep warm on a baking sheet in the oven.
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Serve with a tartar sauce or spicy mayonnaise.