1. Preheat grill to medium-high heat. After preheating, reduce one side to low.
2. Combine 1/4 cup green onions, 1/4 cup shallots, sugar, 2 tablespoons juice, oil, allspice, garlic, and serrano in a mini food processor; process until smooth. Combine half of onion mixture and chicken in a medium bowl; toss well. Sprinkle with salt.
3. Place chicken on grill rack coated with cooking spray over medium-high heat. Cover and grill 5 minutes on each side. Move chicken over low heat. Cover and grill 5 minutes on each side or until done. Brush chicken with remaining onion mixture.
4. Combine remaining green onions, remaining shallots, remaining juice, cheese, cilantro, and sour cream. Halve bell peppers lengthwise; discard seeds. Divide cheese mixture evenly among pepper halves. Place peppers on grill rack coated with cooking spray over medium-high heat. Grill 7 minutes or until peppers are lightly charred.