Mix broth, soy sauce, vinegar, tomato paste, honey, garlic, ginger and dried chiles in a 4-quart slow cooker. Add chicken breasts.
Cover and cook on high for 2 1/2 to 3 hours until the chicken reaches 165°F.
Cook rice during the final hour: bring rice and 1 1/2 cups water to a boil in a covered saucepan, reduce to low and cook for 40 to 45 minutes, then rest covered for 10 minutes.
Lift chicken onto a plate. Stir cornstarch mixed with 2 tablespoons cold water into the cooker and add zucchini and bell pepper. Cover and cook on high for 15 minutes until vegetables are tender and sauce coats a spoon.
Cut chicken into bite-size pieces and return it to the sauce. Remove the whole dried chiles and stir in peanuts.
Divide rice and chicken mixture among 4 bowls.