Separate the cloves of garlic and drop them into a pot of boiling water for 60 seconds—this quick blanching makes them easier to peel. Drain the garlic and peel. Set aside.
Dry the chicken with paper towels (this will help it to brown nicely) and salt and pepper liberally on both sides. Heat the butter and oil in a large pot or Dutch oven over medium-high heat. In batches, sauté the chicken skin side down first, until browned, about 4 minutes on each side. Turn with tongs or a spatula without piercing the skin. When first batch is done, transfer it to a plate and continue to sauté all the chicken in batches. Once the last chicken batch is removed, add all of the garlic to the pot. Lower the heat and sauté for about 7 minutes, turning often so the garlic doesn’t burn and turn bitter. Add the Cognac and the wine, return to a boil, scraping the brown bits from the bottom of the pan. Return the chicken to the pot with the juices and add the thyme leaves and nutmeg. Cover and simmer on low for about 30 minutes, until all the chicken is cooked and tender.
Remove the chicken to a platter and keep warm. In a small bowl, whisk together 1 1/2 cup of the sauce and the flour and then stir it back into the sauce in the pot. Raise the heat, add the cream, and boil for 3 minutes. Add salt and pepper, to taste. Pour the sauce and the garlic over the chicken, sprinkle with parsley and serve with crusty bread. Serves 6 to 8.
Wine pairing: Chardonnay or Pinot Noir