01 - Pat the chicken pieces thoroughly dry with paper towels and season generously with salt and pepper on all sides.
02 - Heat olive oil in a large, heavy-bottomed skillet or Dutch oven over medium-high heat. Sear the chicken pieces skin-side down first, then brown on all sides until deeply golden, about 5 to 7 minutes. Transfer to a plate and set aside.
03 - In the same skillet with the rendered drippings, add the onion and garlic. Cook, stirring occasionally, until softened and fragrant, about 3 minutes.
04 - Add the sliced mushrooms to the skillet and cook until they release their moisture and begin to caramelize, about 5 minutes.
05 - Stir in the tomato paste and cook for 1 minute to deepen its flavor. Pour in the dry white wine, scraping up any browned bits from the bottom of the pan to deglaze.
06 - Add the diced tomatoes and chicken stock, stirring to combine. Return the browned chicken pieces to the skillet, nestling them into the sauce. Bring to a gentle simmer.
07 - Add the tarragon, cover the skillet, and reduce heat to low. Braise for 35 to 40 minutes, 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 added richness and velvety texture. Adjust salt and pepper to taste.
09 - Sprinkle generously with fresh chopped parsley just before serving. Serve alongside buttered noodles, steamed rice, or crusty French bread to soak up the sauce.