How to Make It
In a bowl, blend together the vinegar, mustard, honey, garlic, shallots, salt and pepper. Slowly whisk in the olive oil. Put the chickens in a 2-gallon resealable plastic bag and pour in the marinade. Seal and turn to thoroughly coat the chickens. Refrigerate overnight, turning a few times.
Light 50 charcoal briquettes using a chimney. Run the wand of a thermometer through a cork and use the cork to plug one of the air vents in the grill lid. Leave the remaining lid vents open and adjust the lower vents as needed (if the fire gets too hot, close the vents; too cold, open them).
Combine all of the rub ingredients in a bowl. Combine the wine and apple juice in a spray bottle or small bowl.
Drain the chickens. Set them on a large rimmed baking sheet and sprinkle all over with the rub, inside and out.
When the coals are hot, push them to one side of the grill and set a drip pan half-filled with water on the other side. Using tongs, transfer 4 of the hot coals to the chimney to light an additional 25 briquettes. Set the chickens breast side up on the grill grate over the drip pan, with their cavities facing the coals. Cover and cook for 2 hours, spraying the chickens with the mop every hour. Check the thermometer to maintain a temperature of 250° to 275°. Add more coals, 25 at a time, every hour or so as needed.
After 2 hours, turn the chickens 90°, still breast side up, so their sides are facing the coals. Be careful when turning the chickens to keep the juices inside the cavities. Spray the chickens with the mop. Cover and cook for 1 hour, then turn the chickens so that their opposite sides are facing the coals. Spray again, then cover and cook for 1 to 1 1/2 hours longer, until a thermometer inserted in the inner thigh reads 170°.
Transfer the chickens to a rimmed baking sheet. Pour the cavity juices into a serving bowl. Let the chickens rest for 10 minutes. Cut off the whole legs and transfer them to a platter. Slice the breast meat off the bone and transfer to the platter. Add any accumulated juices to the serving bowl. Serve the chicken with the juices and Kansas City-Style Barbecue Sauce.