Melt butter in a Dutch oven set over medium heat. Add shallots and garlic; cook until transparent, about 3 minutes. Add thyme, bay leaves, and wine. Bring mixture to a boil over high heat.
Add mussels, and cover. Cook, shaking pan often, until mussels open, 5 to 6 minutes. Discard any mussels that fail to open. Using a slotted spoon, transfer mussels to a large bowl, reserving liquid in pan. Sprinkle 1/4 cup parsley over the mussels.
Remove and discard bay leaves and thyme. Return liquid to low heat; stir in creme fraiche and remaining 1/4 cup parsley. Cook just until warm again, and pour over mussels. Serve hot.
Fresh mussels can be stored in the refrigerator, covered with a damp cloth, for one to two days; do not store them submerged in water or they will drown.