Sear the Chicken:
Season chicken with salt and pepper. In a large oven-safe skillet or Dutch oven, heat olive oil over medium-high. Sear chicken skin-side down until golden brown, about 5–6 minutes per side. Remove and set aside.
Sauté the Vegetables:
In the same pan, melt butter. Add onion, garlic, carrots, and mushrooms. Cook for 5–6 minutes until softened and lightly golden.
Build the Sauce:
Stir in flour and cook for 1 minute. Pour in white wine and deglaze the pan, scraping up browned bits. Add chicken broth, cream, mustard, thyme, and bay leaf. Stir to combine.
Return Chicken & Bake:
Nestle chicken thighs into the sauce, skin-side up. Bring to a simmer, then cover and transfer to a preheated oven at 375°F (190°C). Bake for 30–35 minutes, until chicken is cooked through and tender.
Serve:
Remove thyme sprigs and bay leaf. Garnish with fresh parsley. Serve with crusty bread, mashed potatoes, or rice to soak up the sauce.