Combine 1½ pounds chicken thighs, 4 cups broth, 1 cup salsa verde, the chopped bell peppers, poblanos and onion, 1 teaspoon salt and ½ teaspoon each cumin, oregano and garlic powder in a 6-quart slow cooker.
Cover and cook on Low until the chicken is very tender and shreds easily with a fork, 6 hours (or on High for 3 to 4 hours). Transfer the chicken to a cutting board to cool slightly.
Transfer about 1 cup of the broth (with a few vegetables, if desired) to a small bowl. Add 1 cup rinsed beans; mash until mostly smooth. Return the bean mixture to the slow cooker. Stir in the remaining beans. Cover and cook on Low until the beans are heated through, about 15 minutes.
Meanwhile, use 2 forks to shred the chicken. Return the shredded chicken to the soup; stir in 2 tablespoons lime juice.
Ladle the soup into 6 bowls. Garnish with cilantro and/or radishes, if desired. Serve with lime wedges, if desired.
To freeze: Let the soup cool completely. Transfer to airtight freezer-safe containers; freeze for up to 3 months. Thaw overnight in the refrigerator. Reheat in a large Dutch oven over medium-low heat, covered and stirring occasionally, until heated through, 15 to 20 minutes. Garnish with cilantro and/or radishes and serve with lime wedges, if desired.
