Cooking Steps

• Heat 1 tablespoon of the oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the pancetta and cook until crispy, 5 to 8 minutes. Transfer to a paper-towel-lined plate, leaving fat in the pan.
• Season the chicken with 2 teaspoons salt and ½ teaspoon pepper. Brown half the chicken in the pot, skin side down, about 5 minutes. Set aside and repeat with the remaining chicken. Pour off all but about 2 tablespoons of fat.
• Return the pot to medium-low heat. Add onions and cook until softened, 3 to 5 minutes. Add garlic and cook for about 1 minute. Add Cognac and cook until evaporated. Add wine, broth, tomato paste, vinegar, sugar, thyme, bay leaf, and ½ teaspoon salt. Bring to a boil, then reduce to medium and gently boil, uncovered, for 15 minutes.
• Add the chicken and any juices back to the pot with the carrots. Simmer, cover, and cook over low heat for 30 minutes, until cooked through.
• In a skillet, heat remaining oil over medium heat. Add mushrooms and ¼ teaspoon salt; cook until golden brown, about 5 minutes. Set aside.
• In a small bowl, mash butter and flour to make a smooth paste. Set aside.
• Transfer cooked chicken to a plate. Increase heat in the pot to medium. Stir in three-quarters of the butter and flour paste. Boil until thickened, 5 to 7 minutes; add remaining paste if desired.
• Discard the bay leaf. Pull off chicken skin and discard. Return chicken and juices back to the pot and simmer, uncovered, for about 10 minutes. Stir in browned mushrooms and pancetta right before serving.
• Taste and adjust seasoning if necessary, then serve.