Add the chicken breasts, chicken broth, sun-dried tomatoes, onion, garlic, and Italian seasoning to the slow cooker. Stir to combine the ingredients evenly.
Cover and cook on low for 6 hours or on high for 3 to 4 hours until the chicken is fully cooked and tender.
Remove the chicken from the slow cooker and shred it with two forks. Return the shredded chicken to the pot.
Stir in the heavy cream, baby spinach, and Parmesan cheese. Season with salt and black pepper. Cover and cook for 20 more minutes on low until the spinach wilts and the soup thickens slightly.