In a large bowl, stir together the soy sauce, chicken broth, cornstarch, honey, vinegar, ginger, and garlic. Add the chicken and refrigerate for at least 1 hour to marinate.
Heat broiler with the rack 6-inches from the heat. Remove the chicken from the marinade, place on a lightly oiled rimmed baking sheet, and cook for 10 minutes. Flip the chicken and add the broccoli and peppers, pour 3 tablespoons of the marinade over the vegetables, and cook for 10 minutes until the vegetables are tender and the chicken is cooked through. Allow the chicken to rest for 5 minutes, then slice.
Meanwhile, in a small saucepan, pour the remaining marinade and cook over medium heat for 5-6 minutes, until the mixture reaches a boil and thickens. Serve the chicken and vegetables over rice topped with the sauce.