First slice the onion finely and melt it in the butter, stewing it very gently until it is quite soft but still pale yellow.
Meanwhile, put the cleaned mussels in a saucepan with the cider, set them over a fast flame and extract them as soon as they open.
Put the onion mixture, well seasoned, into a long shallow fireproof dish. On top put the sole, skinned on both sides. Through a muslin pour into it enough stock from the mussels barely to cover it.
Cover the dish, and cook in a moderate oven for 15 minutes.
Put the shelled mussels round the fish, and the parsley butter on top of it. Return to the oven for 5 minutes, just sufficient time to allow the mussels to heat through. Serve in the same dish.