Clean mussels thoroughly, debeard them, and discard any cracked or open ones.
Place mussels, shallots, fennel, wine, and 1 tablespoon of parsley in a heavy-bottomed pan.
Cover and cook over high heat for 7 minutes until all mussels have opened.
Strain the mussels into a colander over a bowl and filter the cooking liquid through a clean cloth.
Boil the filtered liquid with cream and lemon juice in a clean pan to reduce by half.
Whisk in the butter and remaining parsley, then season to taste.
Discard any unopened mussels and divide the rest into four soup plates.
Pour the sauce over the mussels, garnish with chopped fennel leaves, and serve.