Place the chicken in a 6-quart slow cooker. Add the cream, broth, cream cheese, butter, garlic, Italian seasoning, salt and pepper.
Cover and cook on HIGH for about 2–3 hours, until the thickest chicken breast reaches 165°F. Start checking at 2 hours; thickness and cooker performance affect timing.
Transfer the chicken to a board and shred or slice it. Keep the cooker on HIGH. Stir the sauce until the cream cheese is smooth.
Add the dry fettuccine, breaking it to fit if needed, and press it into the sauce. Cover and cook about 20–30 minutes, stirring once, until the pasta is tender. If needed, add a small splash of hot water to keep the pasta covered.
Return the chicken, stir in the Parmesan, and heat through. Turn off the cooker and serve as soon as the sauce coats the pasta.