Place the chicken breasts at the base of a slow cooker. Evenly sprinkle with salt, pepper, and garlic powder.
Pour in the heavy cream and chicken broth. Add in the cubed cream cheese, shredded Parmesan, and Italian seasoning. Secure the lid and cook on the LOW setting for 4 to 5 hours, or on HIGH for 2 to 3 hours, until the chicken is fork-tender and fully cooked through.
Once the chicken is done, take it out and shred using two forks. Return the shredded meat to the cooker, stirring thoroughly to achieve a smooth and creamy consistency.
Roughly 20 minutes before serving, cook the fettuccine (or penne) in a separate pot following the package instructions. Drain the noodles completely.
In the final 30 minutes of slow cooker time, stir in the fresh broccoli florets so they gently steam and retain their vibrant color and crisp texture.
Add the cooked pasta into the slow cooker and toss all components together until well-coated in the Alfredo mixture. Stir in butter at this point if a silkier texture is preferred. Serve immediately, garnished with extra Parmesan if desired.