Press "SAUTE" on the Instant Pot and let it heat up for a few minutes, then add in the oil.
Sprinkle both sides of the chicken breasts with salt and pepper, then add to the Instant Pot. Brown chicken for about 3 minutes on each side.
Add garlic, parsley, and chicken broth to the Instant Pot, being sure to scrape the bottom of the Instant Pot with a wooden spatula to remove any burnt bits or pieces from the chicken.
Add the pasta on top of everything and press it gently down into the liquid with a spatula (don't stir it in with the other ingredients). The liquid should barely cover the pasta.
Place the lid on the Instant Pot and turn the valve to "sealing."
Press the "MANUAL" button and cook for 4 minutes.
When the Instant Pot is finished cooking, move the valve to "venting" and do a quick release of the pressure. Remove the lid.
Press the "SAUTE" button and add in the cream cheese, mozzarella cheese, and Parmesan cheese.
In a small bowl, mix together water and cornstarch, then add into the Instant Pot. Stir together until sauce reaches desired thickness and serve.
Top with fresh Parmesan cheese and basil, if desired.