Season the chicken: Pat chicken dry and sprinkle with salt, pepper, and Italian seasoning.
Place in the slow cooker.
Add flavor base: Scatter the minced garlic and butter over the chicken. Pour in the chicken broth.
Slow cook: Cover and cook on Low for 3 to 4 hours, or on High for 2 to 2 1/2 hours, until the chicken is just cooked through and tender. Avoid overcooking.
Shred the chicken: Transfer chicken to a cutting board and shred with two forks.
Return it to the slow cooker.
Add the creamy elements: Stir in heavy cream and cream cheese until the cream cheese melts. Switch the slow cooker to Warm or Low.
Add Parmesan: Stir in Parmesan a handful at a time until the sauce is smooth and glossy. Taste and adjust seasoning.
Cook the pasta: Boil pasta in salted water until just al dente.
Reserve 1/2 cup pasta water, then drain.
Combine: Add pasta to the slow cooker and toss to coat. Loosen with a splash of pasta water if needed for a silky sauce.
Finish and serve: Fold in spinach or veggies if using. Top with extra Parmesan, parsley, and a pinch of red pepper flakes.
Serve warm.