In a medium bowl, whisk together olive oil, lemon juice and zest, soy sauce, rice vinegar, brown sugar, minced garlic, dried oregano, fresh thyme, coriander, paprika, cumin, black pepper, cayenne, and rosemary to form the marinade.
Spatchcock the chicken: place the chicken breast-side down with the backbone facing you and use kitchen shears to cut along both sides of the spine to remove it; flip the bird and press down on the breasts to flatten. Remove wing tips if desired.
Pat the chicken dry with paper towels and season all over with salt.
Gently loosen the skin over the breasts and rub the softened salted butter underneath the skin.
Place the chicken in a large baking dish or shallow container and pour the marinade over it, rubbing it over and under the skin so the bird is well coated. Cover and refrigerate for 2–8 hours.
About 30 minutes before grilling, remove the chicken from the fridge to come closer to room temperature and preheat an outdoor grill to medium-high (about 400°F). Oil the grates lightly.
Set the chicken over indirect heat on the grill, cover, and cook for 45–60 minutes, turning or rotating occasionally for even cooking, until an instant-read thermometer inserted into the thickest part of the breast and thigh reads 165°F.
Remove the chicken from the grill and let it rest on a cutting board for 10 minutes before slicing and serving with grilled vegetables.