Thaw quail, if frozen. (defrost the frozen quail in the refrigerator for 24 hours.) Rinse the quail thoroughly on outside as well as inside the body cavity; pat dry with paper towels. Trim the wing bones from the first joint of the quail; reserve the wing tips for the sauce. Cover quail; refrigerate until needed.
For the sauce, in a Dutch oven, heat the peanut oil over medium heat. Add the reserved wing tips and cook in the hot oil for 3 to 4 minutes or until crispy and browned, turning once.
Add the shallots and garlic and cook, stirring often, for 1 minute. Stir in the 1/2 cup bourbon, 1/4 cup molasses, and the vinegar. Bring to a boil. Lower the heat and simmer, uncovered, until syrupy and the mixture measures 1/4 cup.
Stir in the chicken stock or broth. Bring to a boil. Lower the heat and simmer, uncovered, until the mixture measures 1-1/2 cups, skimming as needed. Add the thyme sprigs and cook for 10 minutes.
Set a fine wire sieve over a medium bowl. Strain the mixture through the sieve; discard the thyme sprigs. Season the sauce to taste with salt and pepper. Set sauce aside until ready to serve.
For the quail, in a small bowl, combine the 2 tablespoons bourbon, 2 tablespoons molasses, and the 2 tablespoons of thyme leaves. Season the inside of each body cavity with a little salt and pepper.
Spoon about 1 teaspoon of the molasses-thyme mixture inside each cavity. Using a knife, make a small crosswise slit at the base of each breastbone. Insert the legs through the slit. Set the quail aside.
In a 12-inch nonstick skillet, heat the oil over medium-high heat. Meanwhile, heat a heavy 10-inch skillet (a cast-iron skillet works well) over medium-high heat for 3 minutes. Place the quail, breast sides down, into the hot oil. Place the second heavy skillet on top of the quail. Lower the heat to medium and cook for 3 minutes.
Remove the heavy skillet; set aside. Using tongs, turn each quail over and cook for 3 to 4 minutes or until the quail are tender and are no longer pink. Meanwhile, in a small saucepan, reheat the sauce.
. To serve, spoon some of the hot cooked rice onto 8 warmed dinner plates at the top center. Then, arrange some of the hot cooked greens in the center of the plate. Place a quail on top and spoon some of the sauce over and around the quail, rice, and greens. Repeat with remaining quail and plates. Garnish each plate with a thyme sprig. Serve immediately. Makes 8 servings.