Coat the interior of the slow cooker with non-stick spray to prevent sticking.
Arrange the chicken breasts evenly at the bottom of the cooker. Distribute the cream cheese cubes over the top, then pour in the heavy cream and chicken broth. Add minced garlic, the Italian seasoning, salt, and black pepper.
Secure the lid and cook on low heat for 4 to 5 hours or on high for 2 to 3 hours, until the chicken is completely cooked through and tender enough to shred.
Remove the chicken from the cooker and use two forks to shred it into bite-sized pieces. Return the shredded meat to the pot and stir in the Parmesan cheese until fully melted and the sauce is smooth and rich.
Roughly 20 minutes before serving, prepare the fettuccine according to the directions on the package. Drain thoroughly.
Add the cooked pasta to the slow cooker and gently toss to coat all the noodles with the creamy chicken Alfredo mixture.
Top with freshly chopped parsley and additional Parmesan if desired. Serve immediately.