Stir together rice wine and grated fresh ginger.
Place scallops in a shallow dish or heavy-duty zip-top plastic bag. Add wine mixture; cover or seal, and chill 30 minutes, turning once.
Soak 6 (12-inch) wooden skewers in warm water 30 minutes. Drain.
Bring 1/4 cup brown sugar, ketchup, chicken broth, rice vinegar, soy sauce, cornstarch, sesame oil, minced garlic, and, if desired, red pepper to a boil in a saucepan over medium heat, stirring constantly. Boil 1 minute; remove from heat, and set aside.
Remove scallops from marinade, discarding marinade. Thread scallops 1/2 inch apart onto skewers.
Grill, covered with grill lid, over medium heat (300° to 350°) 2 to 3 minutes on each side.
Brush scallops with brown sugar sauce, and serve immediately with remaining sauce. Serve scallops over hot cooked rice with chopped fresh parsley. Garnish, if desired.