Combine first 3 ingredients in a large zip-top plastic bag; add quail. Seal and marinate in refrigerator 2 hours, turning bag occasionally. Remove quail from bag, reserving marinade.
Place quail on a broiler pan coated with cooking spray; broil 5 minutes on each side or until done, basting frequently with reserved marinade. Combine pan drippings, reserved marinade, and cornstarch in a microwave-safe bowl; microwave at high for 90 seconds or until mixture boils. Remove skin from quail and discard. Serve sauce with quail.
Note: Semi-boned quail have had the breast bones removed, leaving only the bones in the wings and leg-thigh sections. Some butchers insert wire loops into the breasts to help keep their shape; these should be removed before cooking.