Gather all ingredients. Preheat the oven to 350 degrees F (175 degrees C).
Sprinkle chicken thighs all over with salt and pepper. Heat oil and butter in a large, oven-proof skillet over medium-high heat. Place chicken thighs into the skillet, skin-side down. Cook until skin is golden on one side, 3 to 4 minutes; turn thighs over. Brush with 1 tablespoon mustard and continue to cook until bottom side is golden, 3 to 4 minutes more. Transfer thighs to a plate.
Reduce heat to medium; add sliced onion and remaining ¼ cup of mustard to the skillet. Cook, stirring often, until onions are mostly translucent and evenly coated in mustard, 4 to 5 minutes. Add wine and use a wooden spoon to scrape up any browned bits from bottom of skillet. Increase heat to medium-high and bring to a boil; simmer until sauce reduces slightly and no longer smells strongly of alcohol, about 3 minutes. Add broth, heavy cream, bay leaf, and thyme; stir to combine.
Return chicken, skin-side up, to the skillet and cover. Bake in the preheated oven, until chicken is no longer pink at the bone and juices run clear, about 15 to 20 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
