Set a 6-quart Instant Pot to saute; add olive oil.
Sprinkle chicken evenly with salt, pepper, and Italian seasoning.
When oil is hot, add chicken to Instant Pot. Cook until lightly browned on one side, about 3 minutes.
Turn chicken; add garlic. Cook 1 minute more. Remove with a slotted spoon, and set aside.
Add wine to Instant Pot; stir to release browned bits. Press Cancel to reset Instant Pot.
Add lemon zest and chicken stock to Instant Pot.
Break pasta in half; add to Instant Pot. Place chicken on top of pasta.
Place top on Instant Pot; twist to seal and lock. Turn Steam Release Valve to “sealing.”
Set Instant Pot to cook at High Pressure for 5 minutes.
After cooking is complete, let pressure release naturally for 3 minutes. After that, manually release the pressure by turning the Steam Release Valve to “venting.”
Remove lid from Instant Pot; stir in cream and 1 cup cheese. Place lid back on Instant Pot and let cheese melt, about 3 minutes.
Let pasta mixture rest in Instant Pot 5 minutes; stir to coat noodles in sauce.
Garnish servings with remaining cheese, pepper, and parsley.