Combine basil, broth, cheese, oil, 1/2 teaspoon salt, and garlic in a small bowl.
Sprinkle fish with remaining 1/2 teaspoon salt and pepper. Heat a large nonstick skillet coated with cooking spray over medium-high heat. Add fish; sauté 5 minutes on each side or until fish flakes easily when tested with a fork. Serve fish with the basil mixture.