Place the chicken breasts, chicken broth, chopped carrots, chopped celery, chopped onion, minced garlic, dried thyme, dried rosemary, salt, and black pepper into the slow cooker.
Cover and cook on low for 4 hours, or until the chicken is cooked through and vegetables are tender.
Remove the chicken breasts from the slow cooker and shred them using two forks.
In a small bowl, melt the butter and whisk in the flour until smooth to create a roux.
Add the roux to the slow cooker and stir well to combine.
Return the shredded chicken to the slow cooker and stir in the heavy cream.
Add the potato gnocchi and cook on high for 15 minutes, or until the gnocchi are tender and cooked through.
Stir in the fresh baby spinach and cook for an additional 2-3 minutes until the spinach is wilted.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve hot and enjoy your creamy slow cooker chicken gnocchi soup.