Drain and rinse the black beans. Set one can of the rinsed, drained black beans aside to puree later.
In a blender, combine the reserved can of black beans and 2 cups of the slow‑sodium chicken broth. Puree until mostly smooth. Pour the puree into the slow cooker.
Add the remaining black beans, the remaining chicken broth (the rest of the 3 1/2 cups), the Rotel tomatoes with green chilies, the minced red bell pepper, the 4 oz diced green chiles, 1 tablespoon ground cumin, 1 teaspoon ancho chile powder, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1/4 teaspoon oregano, the 16 oz boneless skinless chicken breasts, and 1/4 cup of the chopped cilantro to the slow cooker. Stir gently to combine.
Cover and cook on HIGH for 4 hours or on LOW for 6 to 8 hours.
When cooking is complete, remove the chicken breasts from the slow cooker and shred them with two forks. Return the shredded chicken to the slow cooker and stir to combine.
Stir in the diced scallions and the remaining chopped cilantro (the rest of the 1/2 cup). Taste and add additional ground cumin if desired.
Serve the soup hot with lime wedges, sliced avocado, and sour cream, if desired.