Add the chicken breasts to the slow cooker.
Layer the diced onion, sliced carrots, sliced celery, minced garlic, and drained cannellini beans over the chicken.
Pour in the chicken broth, then sprinkle the rosemary, thyme, salt, and black pepper on top.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours until the chicken reaches an internal temperature of 165 degrees and shreds easily.
Remove the chicken breasts, shred them with two forks, and return the meat to the slow cooker.
Stir in the fresh spinach and let it sit for 5 minutes until wilted.
Ladle into bowls and top each serving with grated Parmesan cheese.