Spatchcock the chicken: On a cutting surface place chicken breast-side down. Using a pair of sharp kitchen sheers, and starting at the thigh end, cut along one side of the backbone.Turn chicken around and cut along the other side of the backbone to remove it (save the backbone for stock). Flip the chicken over and press firmly on breastbone to flatten the chicken until it is lying completely flat.
Oven instructions: Center a rack in the oven and preheat it to 425 degrees.
Place chicken in a large bowl and pat dry with paper towels. Sprinkle with 3 teaspoons kosher salt -- make sure every crevice is covered. Set aside while you prepare marinade.
If using whole spices, heat a frying pan over medium heat. Add the peppercorns, coriander and cumin seeds; toast until the seeds start to pop, about 2 minutes. Grind them in a small blender, coffee grinder or mortar and pestle.
In a small bowl combine the garlic, lime zest and juice, cilantro, 2 teaspoons salt, and the toasted crushed seeds, or if using ground spices add those to the bowl.
Carefully loosen the skin from the breast and legs of the chicken and, using your clean hands, spread half of the marinade mixture underneath. Rub the remaining mixture all over the outside of the chicken. Place chicken in a large rimmed baking sheet, or skillet, skin side up, and set aside while oven or grill heats up, at least 20 minutes.
Transfer chicken to the oven and cook for 30 minutes. Baste quickly and cook for another 15 minutes or until golden brown and an instant read thermometer registers 165ºF—the time will vary based on the size of your chicken. Transfer to a carving board to rest for at least 10 minutes before cutting.
Grill instructions: Heat grill to medium-high, or set up for indirect heat. Grill chicken, breast-side up for 30 minutes. Flip; cook 15 minutes more. Flip again; grill until internal temperature reaches 165 degrees in thickest part of breast, 5 minutes more. Let rest 10 minutes before carving .
Like ovens, all grills are different and cooking times may vary, so adjust as needed.