Make the marinade: In a food processor, mince the garlic with the salt. Add the ground coriander seeds, ground peppercorns, cilantro stems, soy sauce, and oil; purée until completely blended, 1 to 2 minutes. You'll have about 1 cup marinade. Transfer to a bowl, cover, and set aside (refrigerate it if you're working ahead).
Prepare the chicken: Butterfly the chicken as shown in the photos. Rinse the chicken and dry it with paper towels.
To butterfly a chicken, position the chicken breast side down. With poultry shears or a sharp chef's knife, cut along one side of the backbone and then down the other. Discard the backbone.
Turn the chicken over and press firmly on the center of the breast. You'll need to break the sternum and some ribs for it to lie flat.
Gently separate the breast and thigh skin from the flesh and slip a bit of the marinade under the skin. Then put the chicken and the rest of the marinade in a large zip-top bag, seal the bag, and massage it to distribute the marinade all over the chicken. Marinate the chicken refrigerated, for at least 1 hour and up to 8 hours. Half an hour or so before grilling, take the chicken out of the refrigerator, remove it from the bag, and put it on a platter.
Grill the chicken: Prepare a medium-hot charcoal fire with the coals banked to one side or heat a gas grill to high on one side and medium-low on the other.
Spray the chicken generously with the vegetable oil spray and set it, breast side down, on the hottest part of the grill. Cook the chicken uncovered, turning once, until the skin has deep golden grill marks, 7 to 10 minutes. Move the chicken to the cooler side of the grill. Cover the grill and grill the chicken indirectly, turning every 5 minutes or so, until the juices run clear when the spot between the thigh and breast is pricked and an instant-read thermometer inserted in the thickest part of the thigh registers at least 165°F, another 25 to 30 minutes. Transfer the chicken to a serving platter and tent with foil. Let rest for 5 to 10 minutes. Serve with Sweet & Sour Sauce or let the chicken cool completely and pick off the meat to use in other recipes.