How to Make It
In a small bowl, combine the honey, vinegar, olive oil, minced garlic, ginger, peppercorns, tarragon and thyme.
Rub the mixture over the chickens and put them in a shallow glass dish or stainless-steel pan. Cover and marinate in the refrigerator for at least 3 hours or overnight.
About 30 minutes before cooking, remove the chickens from the refrigerator. Heat the oven to 325°. Remove the chickens from the marinade, but let any marinade that clings to the birds remain. Reserve the rest of the marinade in the refrigerator. Tie the legs of each chicken together. Set the chickens in a large roasting pan and sprinkle with 1 teaspoon of the salt.
Roast the chickens for 45 minutes. Turn the pan and continue roasting until done, about 35 minutes longer. Let cool and then remove the thighs and drumsticks and the breasts and wings from the carcasses. Put them on a baking sheet and refrigerate if not serving immediately. Reserve the carcasses.
In a large pot, heat the cooking oil over moderate heat. Add the onion, carrot, celery and crushed garlic and cook, stirring occasionally, until golden brown, about 10 minutes. Add the chicken carcasses, the stock, wine, water and 1/2 teaspoon of the salt. Add more water if needed to cover the chicken bones. Bring to a boil and skim the foam that rises to the surface. Reduce the heat and simmer for 45 minutes.
Add the reserved marinade and simmer for 20 minutes. Strain the sauce into a medium saucepan. Continue to simmer the sauce until it is just thick enough to coat a spoon, about 20 minutes longer. You should have about 11/4 cups sauce. Whisk in the butter and 1/4 teaspoon of the ground pepper.
When ready to serve, heat the broiler. Reheat the sauce if necessary. Sprinkle both sides of the chicken pieces with the remaining 1/2 teaspoon salt and 1/2 teaspoon ground pepper. Broil, skin-side up, until the chicken is just heated through and the skin is crisp, about 3 minutes. Put a leg and breast on each plate and pour the sauce around the chicken. Scatter the thyme sprigs, if using, over all.