Pat the chicken thighs dry with paper towels. Season both sides with salt and black pepper. Drying the skin helps it brown more effectively and creates a flavorful foundation for the sauce.
Heat the olive oil in a large skillet over medium-high heat. Place the chicken skin-side down and cook for 6–8 minutes until golden brown. Turn and cook for another 3–4 minutes. Transfer the chicken to a plate; it will finish cooking in the sauce.
Reduce the heat to medium and add the butter to the same pan. Add the sliced mushrooms and cook for 5–7 minutes until softened and lightly browned. Stir in the shallots and cook for another 2–3 minutes. Add the garlic and cook for 30 seconds until fragrant.
Stir in the tomato paste and cook for about 1 minute. This deepens its flavor and gives the sauce a richer color. If you prefer a thicker sauce, sprinkle in the optional flour and stir well to coat the vegetables.
Pour in the white wine and gently scrape the bottom of the pan with a wooden spoon to release the browned bits. Let the wine simmer for 2–3 minutes to reduce slightly. This step adds depth and brings together the flavors left behind by the chicken and mushrooms.
Add the chicken stock, chopped tomatoes, thyme, and bay leaf. Stir to combine and bring the mixture to a gentle simmer. Taste the sauce and adjust the seasoning lightly, remembering that it will reduce as it cooks.
Return the chicken thighs to the pan, skin-side up, along with any juices on the plate. Cover partially and simmer gently for 25–35 minutes, or until the chicken is thoroughly cooked and tender. Avoid a vigorous boil, which can make the meat less tender. The thickest part should reach 74°C (165°F), away from the bone.
Remove the bay leaf. If the sauce is too thin, simmer uncovered for a few minutes until it reaches your preferred consistency. Stir in the fresh parsley and optional lemon juice. Taste and adjust the seasoning, then serve the chicken hot with plenty of mushroom-tomato sauce.