Place chicken breasts in the crockpot; season with salt, pepper, and Italian seasoning.
Add sun-dried tomatoes, garlic, olive oil, and chicken broth over the chicken.
Cook on low for 6 hours (or high for 3.5 hours).
Stir in cream cheese, heavy cream, and Parmesan; add spinach on top.
Cook on low another 10–20 minutes until sauce is creamy and spinach wilts.
Shred chicken with two forks in the cooker, stir to coat, and taste for seasoning.
Serve over pasta, rice, or mashed potatoes; garnish with extra Parmesan if you like.