Start wood or charcoal fire or preheat gas grill or broiler.
Cut along each side of the breastbone of each bird, then straight down through where thigh meets body to get 2 semi-boneless halves from each bird. (Don’t worry if skin holding thigh and drumstick together separates.) Combine with all other ingredients in bowl or heavy plastic bag and stir or shake to coat. If time allows, marinate for an hour or so.
Grill quail, turning as needed, until browned and cooked through, about 15 minutes. Serve hot or at room temperature.