Heat butter in a large pot of pan (with a tight fitting lid) over medium heat. Add thinly sliced fennel and a pinch of salt. Sauté until the vegetable begins to caramelize, about 10 minutes.
When the fennel starts browning, add the shallots, which will only take a few minutes to cook through. Add the sliced garlic cloves. Sauté for 2 minutes. Increase burner to medium-high and add wine and stock, bay leaves, salt, pepper and red pepper flakes. Simmer the broth for 5-6 minutes, until it has reduced by half. Reduce heat back to medium and add the heavy cream and cooked green mussels.
Cover the pot and let the mussels heat through - about 3-5 minutes.
Garnish with fresh diced parsley. Serve with lemons, grilled baguette and fries.
