Lightly coat the inside of a 5 to 6-quart slow cooker with nonstick cooking spray.
Place the chicken breasts in the bottom of the slow cooker. Season with Italian seasoning, salt, and black pepper.
Add the minced garlic and pour the chicken broth around the chicken. Arrange the butter pieces over the top.
Cover and cook on LOW for 3 to 4 hours or HIGH for 2 to 3 hours, until the chicken reaches an internal temperature of 165°F.
Remove the cooked chicken and shred it with two forks. Leave the cooking liquid in the slow cooker.
Set the slow cooker to LOW. Add the heavy cream and softened cream cheese. Cover and warm for 15 to 20 minutes, stirring occasionally until smooth.
Gradually stir in the freshly grated Parmesan until incorporated. Avoid boiling the sauce.
Meanwhile, cook the fettuccine in a large pot of salted boiling water according to package directions until al dente. Reserve ½ cup pasta water before draining.
Return the shredded chicken to the slow cooker. Add the drained pasta and gently toss everything together until coated in the creamy sauce.
If needed, add reserved pasta water a tablespoon at a time to adjust the sauce consistency. Garnish with chopped parsley and serve immediately.