01 - Pat the chicken pieces thoroughly dry with paper towels and season generously on all sides with salt and freshly ground black pepper.
02 - Heat olive oil in a large, heavy-bottomed skillet or Dutch oven over medium-high heat. Working in batches if needed, brown the chicken pieces on all sides until deeply golden, about 5 to 7 minutes. Transfer the seared chicken to a plate and set aside.
03 - In the same skillet with the rendered drippings, add the chopped onion and minced garlic. Cook, stirring occasionally, until the onion is translucent and softened, about 3 minutes.
04 - Add the sliced mushrooms to the skillet and continue cooking until they release their liquid and begin to develop a golden brown color, about 5 minutes.
05 - Stir in the tomato paste and cook for 1 minute to caramelize slightly. 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 reduce by half, about 2 minutes.
06 - Add the diced tomatoes and chicken stock to the skillet, stirring to combine. Return the seared chicken pieces to the pan, nestling them into the sauce. Bring everything to a gentle simmer.
07 - Stir in the chopped tarragon. Cover the skillet with a tight-fitting lid, reduce the heat to low, and braise for 35 to 40 minutes, or until the chicken is fall-off-the-bone tender and cooked through to an internal temperature of 165°F.
08 - If desired, stir in the butter for extra richness and velvety texture. Taste the sauce and adjust the seasoning with additional salt and pepper as needed.
09 - Sprinkle generously with fresh chopped parsley just before serving. Present alongside buttered noodles, steamed rice, or crusty French bread to soak up the sauce.