Place chicken breasts (or thighs) in the crockpot. Season with salt, pepper, and Italian seasoning.
In a bowl, whisk together chicken broth, heavy cream, minced garlic, and Parmesan cheese. Pour over the chicken.
Cover and cook on Low for 4 hours or High for 2 hours, until chicken reaches 165°F (74°C) internally.
Remove chicken and shred or slice. For a thicker sauce, mix 1 tbsp cornstarch with 2 tbsp cold water, stir into the crockpot, and cook on High for 10 minutes.
Return chicken to the sauce. Garnish with fresh parsley and extra Parmesan. Serve over pasta, rice, or mashed potatoes.