Prepare the seasoning for the chicken by mincing 4 cloves of garlic and combining this with the leaves from 2 bunches thyme. Add 2 teaspoons pepper and 2 teaspoons salt and crush the mixture to form a paste. Wash and pat the chickens dry. Rub the exterior well with this paste. Clean the carrots, onions, and celery and place the trimmings from these, along with the stems form the thyme, in the cavities of the birds. Pour 6 tablespoons oil into a large roasting pan and place over high heat. Sear each bird on all sides until lightly browned. Transfer the birds to a preheated 375 degree oven and roast for 45 minutes.
Quarter the potatoes and blanch briefly. Quarter the fennel and slice the onions. Cut the celery into 5-inch pieces. Clean the mushrooms and score the tops of each. Pour off all but 4 tablespoons of cooking juices from the birds, after 45 minutes, and toss the vegetables in the juices. Spread them evenly around the birds in the pan and continue cooking the chicken, with the vegetables, for another 30 minutes, shaking the pan several times (or turning the vegetables every 10 minutes). Check to see if chicken is done (leg joint will move easily); remove from oven and let sit 10 minutes before carving.
Meanwhile, roast 8 cloves of garlic (peeled) in the oven, in a little oil, with the chicken, but in a separate dish, for 30 to 40 minutes. Remove and place in a food processor blender with the juice of the lemon, the egg, the leaves from the remaining bunch of thyme, and all but 2 teaspoons minced chives. Pulse these ingredients to blend, then add the olive oil in a steady stream, while the machine is running. Add salt and pepper to taste. Thin the sauce with juices from the chickens. Serve this aioli on the side, sprinkled with remaining chives, with the chickens and vegetables.
