Clean the mussels thoroughly, removing the beards, and discard any that are cracked, or remain open after you tap them sharply against the edge of the sink. Transfer to a large, heavy-bottomed pan with lid.
Add the shallots, fennel, wine and half the parsley. Cover with a lid and cook over a fierce heat for 6-7 minutes, or until all of the mussels have opened.
Lift the mussels out into a colander set over a bowl. Carefully strain the cooking liquor through a clean tea-towel into a separate clean bowl and allow to stand for five minutes so that any sand sinks to the bottom. Discard the vegetables.
Pour the liquor into a clean pan, taking care not to disturb any sand at the bottom. Add any liquor from the bowl below the mussels. Add the cream and lemon juice, and boil to reduce by half. Add the butter and remaining parsley, and adjust the seasoning.
Meanwhile, discard any mussels that remain closed. Divide them between four soup plates, pour the sauce over, sprinkle with fennel leaves (or dill) and serve immediately.