Preheat the grill to medium heat. (When ready to cook, spray the rack--off the grill--with nonstick cooking spray.
In a nonaluminum pan or large shallow bowl, combine the brown sugar, quarter cup water, the vinegar, ketchup, soy sauce, garlic, and ginger. Measure out quarter cup of the mixture and set aside. Add the halibut to the mixture remaining in the pan, turning to coat.
Grill the bell pepper halves, cut-sides up, for 5 minutes, or until the skin is blackened. When cool enough to handle, peel the peppers and cut them into thin strips.
Grill the halibut, uncovered, turning once, for 5 minutes or until the halibut is just opaque. Place the halibut on 4 plates, top with the reserved brown sugar mixture, the bell pepper strips and the scallions, and serve.