If using the chicken brine, prepare it according to the recipe instructions and submerge the whole chicken in it. Let it brine in the refrigerator for the recommended time.
Preheat your grill or smoker to medium-high heat, targeting a temperature of around 375°F (190°C).
In a small bowl, combine the softened butter, minced garlic, minced thyme leaves, minced rosemary leaves, minced parsley leaves, and a pinch of salt and pepper. Mix well until thoroughly combined.
Remove the chicken from the brine (if using) and pat it dry with paper towels.
Stuff the cavity of the chicken with the quartered onion, lemon, and sprigs of fresh rosemary and thyme.
Gently loosen the skin of the chicken by sliding your fingers under the skin, being careful not to tear it.
Spread a generous amount of the herb butter mixture under the skin, covering as much of the chicken as possible.
Rub the remaining herb butter all over the outside of the chicken, ensuring it's evenly coated.
If using a grill, set it up for indirect grilling by turning off one burner (for gas grills) or pushing the charcoal to one side (for charcoal grills). If using a smoker, ensure it's set up for smoking with your preferred wood chips or chunks.
Place the prepared chicken on the grill or smoker over indirect heat.
Close the lid and cook for about 1.5 to 2 hours, or until the internal temperature of the chicken reaches 165°F (74°C) in the thickest part of the thigh, and the juices run clear.
Once done, remove the chicken from the grill or smoker and let it rest for about 10 minutes before carving
Serve the roasted chicken with your favorite sides and enjoy!