Tie the bay leaf and thyme together with kitchen string to make a bouquet garni.
Salt and pepper the chicken on all sides and then coat with the mustard.
Heat a dutch oven over medium high heat until hot. Add the butter and swirl to coat and then place the chicken skin-side down in the pot. Let the chicken brown on one side until the mustard is almost burnt, and then flip and brown the other side. It's okay if some of the browned mustard sticks to the pan and comes off the chicken as you'll be able to scrape it up later after adding the liquids. Transfer the chicken to a plate and set aside.
Add the shallots and onions and saute until tender and browned.
Add the white wine, chicken stock, and bouquet garni and bring the mixture a boil over high heat. Use a spatula to scrape the mustard up off the bottom of the pot. Continue boiling until it no longer smells of alcohol.
Turn off the heat and then return the chicken to the pot along with any accumulated juices. Add the creme fraiche and stir to combine.
Cover with a lid and braise in a 350 degree F (180 C) oven until the chicken easily falls off the bone when prodded with a fork (about 40-50 minutes).
Garnish with parsley and serve with crusty bread, egg noodles, or roasted potatoes.