Remove the parsley leaves from the stems and set aside for later. Finely chop the stems.
Heat a knob of butter in a deep pan and sauté the shallot, garlic, parsley stems, and celery. Add some pepper. No salt is needed because the mussels will add enough salt to the dish.
Add the white wine. Bring to a boil and reduce to two-thirds. Add the mussels and cover the pan. Cook the mussels for 2-3 minutes until 90-95% of them have opened. Remove the mussels from the pan and place them in a separate bowl, leaving the cooking liquid in the pan.
Pour the cream into the liquid. Stir and bring to a boil. Let it reduce again to two-thirds.
Add the mussels back into the pan and mix well. Roughly chop the parsley leaves and add half to the pan. Stir again.
Serve the Moules Marinière on plates and garnish with the remaining parsley leaves. Enjoy!