1. Remove the packets of giblets in the body cavities of the chickens and set aside for another use. Remove and discard the fat just inside the body and neck cavities of the chickens. Rinse the chickens, inside and out, under cold running water and then drain and blot dry, inside and out, with paper towels. Cut each chicken into 10 pieces as show in Preparing the Chicken, Steps 1 through 9 on pages 231 through 233 (4 breast pieces, 2 thighs, 2 drumsticks, 2 wings).
2. Make the marinade: Use your fingers to crumble the saffron into a large nonreactive mixing bowl. Add the water and let stand for 5 minutes. Add the lemon juice, yogurt, oil, parsley, ginger, salt, pepper, and turmeric, if using, and stir until the salt is dissolved.
3. Arrange the chicken pieces in a large nonreactive baking dish and top with the onion. Spoon, the marinade over the chicken and let marinate in the refrigerator, covered, for at least 4 hours or as long a 8, turning several times.
4. Prepare the butter baste: Crush the saffron threads into a saucepan (tilt it slightly), add the water and let stand for 5 minutes. Add the butter, lemon juice, parsley, and pepper and cook over medium heat until the butter melts.
5. Set up the grill for direct grilling and preheat to medium. When ready to cook, brush and oil the grill grate. Place the chicken drumsticks and thighs skin-side down on the hot grate. Cook for 1 to 2 minutes, then add the breast pieces skin-side down. Cook all for 5 to 6 minutes, then turn all pieces over. Continue grilling for 6 to 8 minutes more; you may need to turn the chicken pieces several times to keep them from burning. It's likely the melting fat from the skin will cause flare-ups; move the chicken pieces away from the flames to keep them from burning. The last 2 minutes or so, start basting the chicken with the saffron-herb butter.
6. Transfer the chicken pieces to plates or a platter and garnish with the parsley sprigs. Serve with lemon wedges and sliced red onion.