01 - Pat the chicken pieces dry with paper towels and season both sides generously with kosher salt and freshly ground black pepper.
02 - Heat the olive oil and butter in a large sauté pan or Dutch oven over medium-high heat until the butter foams. Place the chicken skin-side down and sear until deeply golden brown, approximately 5 minutes per side. Transfer the browned chicken to a plate and set aside.
03 - In the same pan with the rendered drippings, sauté the chopped onion over medium heat for 3 to 4 minutes until softened and translucent. Add the minced garlic and sliced mushrooms, continuing to cook until the mushrooms have released their moisture and are lightly caramelized.
04 - Stir in the tomato paste and cook for 1 minute to deepen its flavor. Pour in the dry white wine, using a wooden spoon to scrape up any browned bits from the bottom of the pan. Let the wine simmer and reduce for 2 minutes.
05 - Add the diced tomatoes with their juices, chicken stock, fresh thyme leaves, and bay leaves. Nestle the seared chicken pieces back into the pan, skin-side up, and bring the liquid to a gentle simmer.
06 - Cover the pan with a tight-fitting lid, reduce the heat to low, and cook for 30 minutes, allowing the chicken to braise and become fork-tender.
07 - Remove the lid and continue simmering uncovered for 10 to 15 minutes until the sauce has thickened and concentrated in flavor, and the chicken is cooked through to an internal temperature of 165°F.
08 - Discard the bay leaves. Transfer the chicken to a warm serving platter, spoon the sauce generously over the top, and finish with a scattering of chopped fresh parsley.