In food processor, combine parsley, cilantro, basil and garlic; pulse until finely chopped. Add olive oil, lemon zest, lemon juice, salt, pepper, paprika, cumin, coriander, and hot pepper flakes (optional); puree until smooth. Tip: Substitute 1/8 teaspoon cayenne pepper for hot pepper flakes if desired.
Remove neck and giblets from turkey (reserve for another use). Trim excess fat from turkey and discard. Pat turkey dry with paper towel. Rub turkey all over, including under skin and inside cavity, with 3/4 cup herb sauce. Refrigerate turkey for at least 1 hour or up to 4 hours.
Preheat grill to high; grease grate well. Turn off burners in center of grill and reduce heat to medium (try to maintain temperature of 350°F). For grills with only two burners, cook on one side of the grill over indirect heat.
Place turkey breast side up, on center of grill. Cook, covered, over indirect heat, basting with remaining herb mixture, for 2.5-3 hours or until thermometer inserted into thickest part of the breast reaches 170°F.
Carefully transfer turkey to cutting board and tent loosely with foil. Let stand for 30 minutes before carving.