Place the chicken breasts in the bottom of the slow cooker. Pour the chicken broth over the top.
Add the minced garlic, Italian seasoning, salt, pepper, and sun-dried tomatoes. Stir lightly to distribute the seasonings.
Cover and cook on low for 6 hours or until the chicken reaches an internal temperature of 165°F.
Remove the chicken and shred it with two forks, then return it to the slow cooker.
Stir in the heavy cream, spinach, and Parmesan cheese. Cover and cook on low for another 20 to 30 minutes until the spinach wilts and the sauce thickens slightly.