Traditionally, this dish is cooked in a covered casserole; the flesh ends up succulent but the skin will not brown. For the sake of flavorful skin, we opt to brown the chicken before cooking. If you are not a chicken skin aficionado, feel free to skip this step.
Position a rack in the center of the oven. Preheat the oven to 375°F.
Have ready:
If using a whole bird, remove the neck and giblets and cut the chicken into 10 pieces (see About Cutting Up Raw Poultry). Season the chicken with:
Heat in a Dutch oven over medium-high heat:
Add the chicken pieces in batches and brown well on both sides. Transfer to a plate and add to the pot:
Bring to a boil, using a wooden spoon to scrape any browned bits off the bottom of the pot. Return the chicken pieces to the pot, skin side up, cover, and transfer to the oven. Bake for 20 minutes. Increase the oven temperature to 450°F, uncover the pot, and cook the chicken until the internal temperature of the breast pieces reaches 160°F, about 25 minutes. Transfer to a plate and simmer the thighs and drumsticks until they reach 175°F, about 10 minutes longer. Return the breasts to the pot when all of the pieces are done. Make sure there is always some liquid in the bottom of the pot; add a little more wine or stock if needed.
Remove the chicken and garlic from the pot and keep warm. Skim as much fat as possible from the pan juices with a spoon. If the pan juices are watery or weak in flavor, boil them down over high heat to concentrate. Peel 10 of the garlic cloves and mash to a paste, then stir into the sauce and boil for 1 minute. Take the sauce off the heat. If desired, stir in:
Season to taste with:
Arrange the chicken on a platter. Spoon the sauce over it and scatter the garlic cloves around it.