In a small pot, whisk together broth, lemon juice, and cornstarch. Let boil for 1 minute, stirring continually. Take pot off of heat and whisk in parsley, salt, oregano, and rosemary. Reserve in a warm place.
Lay fish on a cooking spray coated grill rack. Place lid on grill and cook 6 minutes per side, fish will flake easily when finished. Spoon sauce over fish or serve on the side.