Cut chiles in half; discard seeds and membranes. Place halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 5 minutes or until blackened. Place in a heavy-duty zip-top plastic bag; seal. Let stand 15 minutes. Peel chiles; discard skins. Chop chiles.
Heat oil in a large Dutch oven over medium-high heat. Add chicken; cook 4 minutes on each side or until browned. Remove chicken from pan. Add onion and garlic, and sauté 6 minutes or until browned, stirring frequently. Return chicken to pan. Add broth, 1 1/2 cups water, and cumin; bring to a simmer. Cook 20 minutes or until chicken is done. Remove chicken; cool slightly. Remove chicken from bones; cut meat into bite-sized pieces. Discard bones. Add chicken to pan; stir in chopped chiles and beans.
Combine 1/2 cup water and flour, stirring with a whisk. Stir into chicken mixture. Bring to a simmer; cook 15 minutes. Stir in salt. Spoon about 1 1/2 cups soup into each of 6 bowls; top each serving with 1 1/2 teaspoons sour cream. Serve with lime slices.