In a large pot melt the butter over medium flame, add shallots and garlic and saute for 5 minutes. Add fennel or celery and continue to saute for 2 minutes. Add the mussels and raise the heat to high. When mussels begin to open, add the wine, salt, pepper and bring the mixture to a boil, cover and cook until all mussels open up. Discard any unopened ones. Stir in half of the garlic butter, the parsley and the chopped fennel fronds. Serve with remaining garlic butter on the side.
Place all in the food processor and blend for 20 seconds until well mixed, or blend in a bowl.
Cover and place in refrigerator until ready to use.