Whisk together Italian dressing, mustard, mayo, lime zest, and optional Worcestershire or pickle brine until smooth.

Pat split chicken halves dry with paper towels.

Brush a thin, even coat of binder over all sides of the chicken, including under the skin where possible.

Place chicken skin-side up on a rack over a tray.

Rest uncovered in the fridge for 30–45 minutes. This sets the binder and helps the skin tighten.

Mix all rub ingredients.

Remove chicken from fridge and season generously on all sides. Press lightly to help it stick.

Let the chicken rest at room temperature for 15 minutes.

Set up a two-zone fire (375–400°F in the cool zone).

Start chicken skin-side up over the cool side for 10 minutes to set the rub.

Move chicken over the coals and grill, flipping every 10 minutes. Slide to the cool side occasionally to let fat render without burning.

Continue until internal temp is 155–160°F in the breast and 170–175°F in the thigh.

Let chicken rest 5–10 minutes.

Squeeze fresh lime over each half. Garnish with parsley or cilantro if desired.