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1
Cook shallots in oil in a 4-quart heavy pot over moderately low heat, covered, stirring occasionally, until soft, 12 to 14 minutes (reduce heat to low if shallots begin to brown).
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2
Stir in vinegar, tomato puree, honey, steak sauce, Worcestershire, salt, and pepper and bring to a boil.
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3
Remove sauce from heat and reserve 1 1/2 cups for basting and 1 cup for serving.
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4
Cool sauce to room temperature before brushing on chicken (sauce will thicken as it cools).
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5
Remove excess fat from chicken and pat chicken dry.
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6
Brush all over with some barbecue sauce and season with salt and pepper.
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7
Open vents on bottom of grill and on lid.
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8
Light a large chimney of charcoal briquettes (about 100) and pour them evenly over 1 side of bottom rack (you will have a double or triple layer of charcoal).
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9
When charcoal turns grayish white (15 to 20 minutes from lighting) and you can hold your hand 5 inches above top rack for 3 to 4 seconds, sear chicken on lightly oiled grill rack over coals, uncovered, turning, until well browned, about 3 minutes total.
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10
Move chicken to side of grill with no coals underneath, arranging skin sides up, then cook, covered with lid, brushing with sauce and turning every 10 minutes, until cooked through, 45 minutes to 1 hour.
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11
Preheat all burners on high, then adjust heat to moderate.
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12
Sear chicken on lightly oiled grill rack, uncovered, turning, until well browned, about 10 minutes total.
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13
Adjust heat to low, then cook chicken, covered with lid, brushing with sauce and turning every 10 minutes, until cooked through, about 25 minutes.
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14
Serve chicken with reserved cup sauce.
