In a large frying pan, melt the butter over medium heat, and cook until it is just beginning to turn brown. Add the onions and celery to the pan, and cook just until the onions are clear.
Place mussels in pan, and stir. A few minutes after the mussels start releasing their juice, pour wine over them. Add the sprigs of thyme and the bay leaves; stir, then add salt and pepper. Continue to cook for about 10 more minutes, stirring frequently.
Once all of the mussels are open, stir two large spoonfuls of creme fraiche into the sauce. Divide mussels and sauce between four bowls, and add a bit of parsley and another very small spoonful of creme fraiche for decoration.
