Bring a small saucepan of water to a boil. While the water heats, separate the cloves of garlic, then add them to the boiling water. Boil for 1 minute. Drain the garlic and peel the cloves, discarding the skins. Set aside.

Rinse the chicken pieces under cold water, then pat dry with paper towels. Season liberally with salt and pepper. In a large pot or Dutch oven over medium-high, heat the butter and oil.

In batches, saute the chicken, skin side down first, until nicely browned, about 3 to 5 minutes on each side. To prevent piercing or tearing the skin, use tongs or a spatula to turn the pieces.

As it cooks, transfer the chicken to a plate and set aside. Without cleaning the pot, add the garlic, reduce heat and saute for 5 to 10 minutes, or until the cloves are evenly browned.

Add 2 tablespoons of cognac and all of the wine. Bring to a boil and scrape the brown bits from the bottom of the pan. Add all of the chicken to the pot, along with any juices in the plate, and sprinkle with the thyme leaves.

Cover and simmer over the lowest heat for about 30 minutes, or until the chicken is cooked through. Transfer the chicken to a platter and cover with aluminum foil to keep warm.

In a small bowl, whisk together the flour and 1/2 cup of the liquid from the pot. Pour this mixture into the pot and whisk into the remaining liquid and garlic cloves. Increase the heat to medium, add the remaining cognac and the cream. Bring to a boil and cook for 3 minutes.

Season with salt and pepper. Pour the sauce and the garlic over the chicken and serve hot.