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Put the potatoes in a pan of cold, salted water. Bring to a simmer and bubble for 10 mins, or until just tender. Heat oven to 200C/180C fan/gas 6. Drain the potatoes, tip into a large roasting tin (big enough to fit the fish), and toss in 1 tbsp oil and some seasoning. Roast for 15 mins.
Make a couple of slashes in the side of each fish. Rub the remaining oil, the lemon zest, fennel seeds and some seasoning into the flesh and cavity of the fish. When the potatoes have had their cooking time, remove the tray from the oven, make space in the centre and place the fish on the tray. Poke the lemon slices into the cavities of the fish. Scatter the chorizo over the potatoes and pour over the wine. Return to the oven for a further 15 mins.
Check the fish is very nearly cooked – the flesh should pull away from the bones easily when gently pushed with a knife. Scatter the peas and broad beans around the fish, mix through the potatoes and chorizo and return to the oven for 2 mins more, to just warm the veg through. Scatter over the parsley just before serving.