Preheat the oven to 375 degrees.
Heat the duck fat in a cast iron skillet over medium high heat.
Season the chicken thighs with salt and pepper.
Add the thighs to the skillet and brown on both sides, about 3-5 minutes each side.
Remove the chicken from the skillet and set aside. Lower heat to medium and add the garlic, shallots and thyme.
Cook 1-2 minutes, or until lightly browned.
Add white wine to deglaze and cook for 2 minutes.
Add the broth and mustard and bring to a boil. Cook for 2-4 minutes.
Remove from heat, add the chicken thighs, and place skillet directly in the oven. Cook for 30 minutes.