Boil all the vegetables in well-salted water till just tender. Drain and refresh in cold water. This can be done some time before making the dish. You will need to construct some sort of steamer for this dish.
Cut the fillets of fish into 4 equal portions. Season with salt. Place the John Dory and turbot in the steamer and steam for about 6 minutes. Remove the fish from the steamer and keep warm. Put the vegetables in the steamer to warm through for a couple of minutes. While you are steaming the fish, take a frying pan, add the olive oil and season the red mullet with salt and pepper and fry for 4 minutes, skin-side down. Remove and keep warm with the other fish. Add the vermouth to the frying pan and boil off for 1 minute. Then add the fish stock and the crème fraîche and reduce to a sauce which will coat the back of a spoon. Lay the fish on 4 warm plates all together on one side of the plate and a pile of vegetables on the other. Pour the sauce over the fish, decorate with the sprigs of parsley and serve.
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