Rinse and clean the mussels, removing small bits of seaweed or debris from the shells. Fresh mussels should be tightly closed and smell of the sea, so be sure to discard any that are open or cracked.
In a very large pot over medium heat, melt the butter with the oil, add the shallots, and cook until tender. Add the herbes de Provence and thyme, then add the Pernod and deglaze the pan. Increase the heat to high and add the white wine. Bring the liquid to a full rolling boil, then add the mussels and cover. Wait for 3 minutes and then shake the pot from side to side. Remove the cover and turn the mussels around in the pot with a slotted spoon, pulling the open ones to the top. Cover again and cook for 3 more minutes.
Mussels usually take 5 to 8 minutes in total to cook. Small ones will cook very quickly and if overcooked will have a mealy texture. Once the majority are opened, you can remove the cooked mussels with a slotted spoon and place them in a large serving bowl. Be sure to discard any mussels that do not open.
Add the cream to the cooking broth and reduce for about 5 minutes or until the sauce is creamy and sticks to the back of a spoon. Ladle the hot creamy sauce over the mussels and then pour the rest into a small pitcher to serve table side or to reheat for second courses. Always serve with plenty of fresh baguette to soak up the delicious sauce and plenty of napkins!