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ROAST CHICKENS:
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Open vents on bottom of grill. Light a fire well over to one side of grill, using enough charcoal to fill 1 1/2 large shoeboxes (about 90 briquettes).
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Stir together ketchup, brown sugar, coriander, and cumin in a small bowl.
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Push down hard on each chicken (breast side up) to flatten it as much as possible.
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Season chickens generously with kosher salt and pepper and coat thoroughly with ketchup mixture.
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When flames have all died down and coals are covered in white ash, place chickens, breast sides down, on side of grill away from coals, legs facing away from coals (be careful that none of meat is directly over coals). Put lid on grill with vents open one quarter of the way. Roast 30 minutes, then turn chickens over and add another 1/2 shoebox (about 30 briquettes) of new charcoal. Continue roasting 45 to 50 minutes more. To check for doneness, cut into thickest part of a thigh, all the way to bone; there should be no sign of pink. (It's not easy to take the temperature of a flattened bird, but if you do use a thermometer, look for a final temperature of 170u00b0F in fleshy part of thighs; do not touch bone.) Transfer chickens to a carving board and loosely cover with foil.
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Let chickens stand about 10 minutes before cutting into serving pieces.
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MAKE BARBECUE SAUCE WHILE CHICKENS ROAST:
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Bring cider, vinegar, zest, brown sugar, and celery seeds to a boil in a small saucepan. Simmer over low heat, stirring frequently, until thick, syrupy, and reduced by about two thirds, about 20 minutes. Serve with chicken.
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COOKS' NOTE: Barbecue sauce can be made 2 days ahead and chilled. Reheat before serving.
