Add chicken broth, uncooked pasta, chicken pieces, garlic, Italian seasoning, salt, and pepper to the Instant Pot. Stir gently to combine, making sure pasta is submerged.
Close the lid, set the valve to sealing, and cook on high pressure for 5 minutes.
When cooking is complete, do a quick release of the pressure.
Open the lid and stir the pasta. It should be tender and most of the liquid absorbed.
Turn off the Instant Pot and stir in the heavy cream, butter, and Parmesan cheese.
Let the mixture sit for 3-5 minutes to thicken—the sauce will continue to thicken as it cools.
Stir well, garnish with fresh parsley if desired, and serve immediately with extra Parmesan on the side.