Preheat the oven to 350 degrees F (175 degrees C).

Warm oil and butter in a large, ovenproof casserole or Dutch oven over medium-high heat. Season chicken thighs with salt and pepper and place into the pot, skin-side down. Brush thighs with 1/2 the mustard. Cook until skin is golden, 3 to 4 minutes, and turn thighs over. Brush with remaining mustard. Cook 3 to 4 minutes more and transfer thighs to a plate.

Reduce heat to medium and add sliced onion to the casserole. Cook until nearly clear, 5 to 6 minutes. Pour in wine to deglaze. Increase heat to medium-high and bring to a boil, about 5 minutes. Keep cooking until sauce reduces slightly and no longer smells strongly of alcohol, 3 to 4 minutes more.

Pour broth and heavy cream into the casserole dish. Scrape the bottom to loosen browned bits. Add bay leaf and thyme. Return chicken to the casserole dish and cover.

Bake in the preheated oven until chicken is no longer pink at the bone and juices run clear, about 40 minutes.