Preheat oven to 375°F.
Heat a large cast iron skillet over medium heat for 1 minute and add the oil. Heat the oil until shimmering but not smoking.
While the oil heats, season both sides of the chicken with salt, pepper and Herbes de Provence.
Cook the chicken, skin-side down until the skin is crispy and golden brown, about 5-6 minutes. Flip the thighs over and cook another 4 minutes. Transfer the chicken, skin-side up, to a paper towel-lined plate and set aside. Leave 1-tablespoon oil in the skillet and discard the rest.
Set the heat to medium-low and add 1 tablespoon butter to the skillet. Add onion and sauté about 3-4 minutes or until translucent.
Add the garlic and cook another 30 seconds, stirring often.
Slowly add the wine to the skillet and stir (scraping to deglaze any tasty brown bits stuck to the skillet).
Add the broth, cream, three mustards, and thyme leaves. Season with salt and pepper and stir well.
Nestle the partially cooked chicken (skin-side up) in the skillet with the sauce. Be sure to leave a little space between each thigh for the sauce to seep through.
Cook, uncovered, at 375°F for 30-35 minutes, or until the chicken reaches 165°F. The sauce should have reduced about halfway.
Serve the chicken with the reduced pan sauce.