Season the chicken with salt and pepper. Dredge in flour, shaking off the excess. In a large skillet, melt the butter with the olive oil over medium-high heat. Sear the chicken on both sides until golden brown. Remove from the skillet and set aside.
In the same skillet, sauté the diced onion, minced garlic, sliced carrots, celery, and mushrooms until softened.
Add the white wine and let it reduce for a few minutes, scraping up any browned bits from the bottom of the pan. Pour in the chicken broth, add the thyme and bay leaves.
Return the chicken pieces to the skillet, cover, and simmer over low heat for 25-30 minutes, or until the chicken is cooked through and tender.
Once the chicken is tender, stir in the heavy cream and simmer for another 5-10 minutes, until the sauce has thickened and become creamy.
Serve hot, garnished with fresh parsley. Serve with cooked rice, mashed potatoes, or fresh bread.
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