Slice chicken lengthwise into 2 to 3 equal portions, about 1 1/2-inch wide. Combine 1 Tbs. brown sugar, 1 tsp. minced ginger, juice from half an orange, 2 Tbs. sesame oil, 1 Tbs. soy sauce, and scallion whites in a shallow bowl; add chicken and turn to coat. Let marinate in the refrigerator until ready to grill, or up to 4 hours.
In a small saucepan over medium-low heat, combine plum and apricot jam. Stir in 1 Tbs. vinegar, 2 Tbs. brown sugar, 1 tsp. minced ginger, orange zest, a pinch of salt and 1/4 to 1/2 cup water to thin. Stir often and heat through for approximately 15 minutes.
In a blender or food processor, mix peanut butter, 1 Tbs. soy sauce, 1 tsp. sesame oil, 1 Tbs. vinegar, remaining orange juice, and 1/4 to 1/2 cup water until smooth.
Preheat grill to medium-high. Remove chicken from marinade and weave each slice of chicken onto skewer. Wrap exposed portion in foil before grilling to prevent burning.
Grill about 1 to 2 minutes per side or until cooked through. Remove from grill and sprinkle with scallion greens. Serve with plum and peanut dipping sauces.