Prep the slow cooker: Lightly grease the insert with olive oil or spray. This helps prevent sticking and makes cleanup easier.
Layer the aromatics: Add the chopped onion and minced garlic to the bottom of the slow cooker.
Sprinkle in the lemon zest, Italian seasoning, salt, pepper, and red pepper flakes if using.
Add chicken and liquids: Place the chicken on top. Pour in the chicken broth and half the lemon juice. Dot the butter around the chicken.
Cook low and slow: Cover and cook on Low for 3.5 to 4.5 hours or High for 2 to 3 hours, until the chicken is tender and easily shredded.
Avoid overcooking to keep it juicy.
Shred the chicken: Remove the chicken to a plate and shred with two forks. Return it to the slow cooker and stir to coat in the lemony juices.
Make it creamy: Stir in the cream cheese (if using) until melted and smooth. Then add the cream or half-and-half and the Parmesan.
Taste and add more lemon juice, salt, or pepper as needed.
Cook the pasta: Boil the pasta in salted water according to package directions until just al dente. Reserve about 1/2 cup of pasta water, then drain.
Combine: Add the drained pasta to the slow cooker and toss well with the chicken and sauce. If it seems thick, loosen with a splash of pasta water.
Finish and serve: Stir in parsley.
Plate with extra Parmesan and lemon wedges. Serve warm.