Combine softened butter, minced garlic, lemon zest, lemon juice, fresh parsley, fresh thyme, fresh rosemary, salt, and pepper in a bowl. Mix until fully combined.
Place the chicken breast-side down. Cut along both sides of the backbone with poultry shears, remove it, flip the bird over, and press the breastbone flat. Save the backbone for stock.
Pat the chicken thoroughly dry. Loosen the skin over the breasts and thighs. Spread half the compound butter under the skin and rub the rest across the outside. Season generously with salt, pepper, garlic powder, onion powder, and paprika.
Set up the grill for indirect cooking at 375°F. On charcoal, pile coals on one side. On a pellet grill, set the dial. On gas, light the outer burners only.
Place the chicken skin-side up on the indirect zone. Close the lid and cook 50-70 minutes depending on bird size. Optionally baste with melted herb butter in the final 15 minutes.
Check internal temperature: 160°F in the thickest part of the breast and 175°F in the thigh. The temperature will rise about 5°F during the rest.
Rest the chicken 10-15 minutes before slicing. Serve with grilled vegetables, roasted potatoes, corn on the cob, or fresh salad.