To make the sauce, put the fish stock and Noilly Prat into a saucepan and boil rapidly until reduced by three-quarters to about 180ml/6¼fl oz. Now add the cream and continue to boil for two minutes. Remove from the heat and set aside.
Peel the cucumber and then cut in half lengthways. Scoop out the seeds with a melon baller or teaspoon and then cut each half across into slices 1cm/½inch thick.
Preheat the grill to high. Melt the 25g/1oz butter in a large heavy-based frying pan. Brush the John Dory fillets with a little of the butter, season on both sides with salt and freshly ground black and white pepper. Place skin-side up on a lightly greased baking tray and set aside.
Heat the remainder of the 25g/1oz butter until foaming, add the prepared cucumber and cook over a high heat for 1-2 minutes, shaking the pan every now and then, until lightly coloured. Season with salt and freshly ground black and white pepper and remove from the heat.
Grill the fillets of John Dory 2-3 minutes for those from the smaller fish, five minutes for those from the larger, until the skin is lightly browned and the fish is just cooked through.
Bring the sauce back to the boil and whisk in the chilled, cubed butter, a few pieces at a time. Season to taste with a little salt.
To serve, place the John Dory fillets into the centre of four warm plates. Spoon the cucumber alongside the fish and sprinkle with the basil. Spoon the sauce over the cucumber and around the outside edge of the plates.
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