Stir the broth, mustard, lemon juice and black pepper in a small bowl.  Reserve 3/4 cup broth mixture for the sauce.  Pour the remaining broth mixture into a shallow nonmetallic dish or gallon-size resealable plastic bag.  Add the fish and turn to coat.  Cover the dish or seal the bag and refrigerate for 1 hour.  Remove the fish from the marinade.
Lightly oil the grill rack and heat the grill to medium.  Grill the fish for 10 minutes or until cooked through, turning the fish over once halfway through the grilling time and brushing often with the marinade.  Discard the marinade.
Stir the cornstarch and the reserved broth mixture in a 1-quart saucepan.  Cook and stir over medium heat until the mixture boils and thickens.  Serve the sauce with the fish.