Add the chicken to a 6-quart crockpot. Season with Italian seasoning, salt, and pepper. Add the heavy cream and broth. Scatter the cubes of butter and minced garlic over the top of the chicken.
Cover and cook on high for 2 hours, until the chicken is cooked through and 165°F internally. Remove the chicken and place it on a cutting board. Slice or chop when cooled.
To the slow cooker, stir in the grated Parmesan cheese until combined. Add the dry pasta, toss and ensure it is all covered, and continue to cook on high for about 20 minutes.
When the pasta is nearly cooked, return the chicken to the crockpot and heat through. Turn off the heat and allow to cool a bit to thicken the sauce, then serve garnished with Parmesan cheese and parsley, if desired.
