How to Make It
In a large resealable plastic bag, mix the yogurt with the cilantro, lemon juice, garlic, cayenne, cumin, 2 teaspoons of salt and 1 teaspoon of pepper. Add the chicken halves and turn to coat. Seal the bag and transfer to a baking dish. Refrigerate for at least 3 hours or overnight. Bring the chicken to room temperature before grilling.
Set up a gas grill for indirect grilling, then heat to 400° and oil the grate. Remove the chicken from the marinade, scraping off any excess; discard the marinade. Season the chicken with salt and pepper. Set the chicken skin side up on the grate over indirect heat. Close the grill and cook, turning once, until the chicken is browned and nearly cooked through, about 25 minutes; use a spray bottle filled with water to stop flare-ups.
Reduce the heat to moderately low. Flip the chicken and grill it over direct heat, turning occasionally, until lightly charred and an instant-read thermometer inserted in the inner thighs registers 160°, about 15 minutes more. Transfer the chicken to a carving board and let rest for 10 minutes before carving.