½ teaspoon kosher salt
¼ teaspoon ground black pepper
2 tablespoons olive oil
1 onion, finely chopped
¼ pound white button mushrooms, quartered
3 garlic cloves, finely minced or pressed through a garlic press
1 tomato, cored, halved, and chopped, or ¾ cup canned chopped tomatoes
1 tablespoon all-purpose flour
1 teaspoon dried tarragon
½ cup dry white wine
1 cup chicken broth, plus extra if needed
¼ cup Dijon mustard
2 tablespoons sour cream
1. Preheat the oven to 350°F. Place the chicken on a cutting board and remove and discard the skin. Season the meat with the salt and pepper. Heat 1 tablespoon of the olive oil in a heavy-bottomed pot or Dutch oven over medium-high heat. Add the thighs, smooth side down, and cook until browned, about 4 minutes. Turn over the thighs and brown the other side, about 3 minutes more. Transfer the chicken to a plate and set aside.
2. Add the remaining 1 tablespoon olive oil along with the onion and cook until soft, stirring occasionally, for about 5 minutes. Stir in the mushrooms and continue to cook until the mushrooms are soft, 3 to 5 minutes. Add the garlic and cook until fragrant, 1 to 2 minutes, and then add the tomato and flour and cook, stirring, until the tomato begins to break down, about 3 minutes. Stir in the tarragon. Raise the heat and pour in the wine, letting it simmer for 1 minute before returning the chicken to the pot. Pour in enough broth to reach halfway up the sides of the chicken, then cover the pot and place it in the oven to braise, until the chicken pulls away from the bone easily, about 45 minutes, removing the lid halfway through cooking.
3. Remove the pot from the oven, use tongs to transfer the chicken to a plate, and set aside. Add the mustard and sour cream (if using) to the sauce and stir to combine. Then return the chicken to the pot and cook for about 5 minutes to bring the flavors together before serving.