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Bring a saucepan of salted water to the boil, add the potato and parsnips, and boil until almost tender – about 4 mins. Drain well.
Meanwhile, put the fish in a pan where they will fit snugly but not on top of each other. Cover with the milk, poke in the parsley stalks and bring the milk to a gentle simmer. Cover the pan, turn off the heat and leave to sit in the milk for 5 mins. Lift the fish out and break into large chunks. Discard the parsley stalks but keep the milk.
Put the spring onion whites, milk and flour in a saucepan together. Bring to a simmer, whisking continuously, until the sauce has thickened and become smooth. Turn the heat down, add the drained potatoes and parsnips, the lemon zest and half the juice, and cook gently for 5 mins, stirring occasionally. Stir in the spring onion greens, fish and parsley, and taste for seasoning – it will need plenty of pepper, some salt and maybe more lemon juice from the leftover half. Divide between two shallow bowls, serve with chunks of crusty bread and enjoy.