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, 1/4 cup water, the vinegar, ketchup, soy sauce, garlic, and ginger. Measure out 1/4 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.