Heat the olive oil in a large pot over medium. Add the onion, carrots, and garlic, and cook until softened, about 5 minutes. Add the broth, chicken, and beans. Bring to a boil, turn the heat to low and simmer, covered, until the chicken is cooked through, about 20 minutes. Remove the chicken from the soup and use two forks to shred. Return the chicken to the soup. Add the spinach and season to taste with salt and pepper. Ladle into soup bowls and top with Parmesan.