Place beans, garbanzo beans, chicken, broth, carrot, celery, onion and garlic powder in slow cooker.
Cover and cook on low for 4-6 hours, or until chicken is tender. Remove the chicken and place on a cutting board. Cut the chicken into small bite-size pieces. Add chicken back into slow cooker.
Add in pesto and stir.
Ladle soup into bowls and top each bowl with a tablespoon of Parmesan cheese.