Preheat broiler for at least 15 minutes.
Place chicken halves on a baking sheet. Broil chicken halves, turning once, until skin is golden brown and juices run clear when bird is pierced with a fork, about 30 minutes. Remove chicken from broiler, leaving broiler on. Using a very sharp knife, cut each half into about 6 pieces (leg, thigh, wing, 3 small breast pieces).
Place chicken on a rimmed baking sheet in a single layer. Pour lemon sauce over the chicken, and toss until well coated.
Return to broiler, and broil for 3 minutes. Turn chicken pieces and broil for 1 minute more Remove from broiler, and divide chicken between 6 plates.
Pour sauce into heavy saucepan, and stir in parsley. Place over high heat and boil for 1 minute. Divide sauce between plates and serve immediately.
Place all ingredients in a large bowl and whisk until well combined. Cover, and refrigerate until ready to use. Whisk, or shake vigorously before using.;
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