Begin by placing the boneless chicken breasts in the bottom of your slow cooker. Generously season the chicken with sea salt, freshly ground black pepper, and Italian seasoning to infuse flavor.
Sprinkle the minced garlic over the chicken, then pour the chicken broth on top. Secure the lid on the slow cooker and set it to cook on low for 4-5 hours, or until the chicken is fork-tender and fully cooked through.
Once the cooking time is complete, carefully remove the chicken from the slow cooker and use two forks to shred it into bite-sized pieces. Return the shredded chicken back into the slow cooker, mixing it with the broth.
Now, pour in the heavy cream and add the freshly grated Parmesan cheese. Stir the mixture until the cheese melts and combines smoothly with the cream. If you opted for greens, add the broccoli florets or spinach at this point, stirring to incorporate.
Gently add the uncooked fettuccine pasta to the slow cooker, pressing it down slightly into the creamy sauce to ensure it’s submerged. Re-cover the slow cooker and cook on low for an additional 30-40 minutes, or until the pasta is perfectly tender.
After the pasta has cooked, take a moment to stir the mixture thoroughly, ensuring every strand of fettuccine is coated in the rich Alfredo sauce. Taste your dish and adjust the seasoning with an extra dash of salt or pepper as needed.
To serve, ladle the creamy chicken Alfredo into bowls and garnish generously with finely chopped fresh parsley.