Place chicken, penne, broth, broccoli, butter, Italian seasoning, salt, and pepper into an Instant Pot®. Place the lid on the pot and click into place to close. Press the Pressure Cook button and adjust the timer to 5 Minutes.
When the timer beeps, quick-release the pressure until float valve drops. Unlock lid. Pour in milk and cream, stirring quickly until well combined.
While the Instant Pot® is on Keep Warm mode, sprinkle in Parmesan and continue stirring until sauce begins to thicken and coat pasta, about 2 Minutes. Serve warm.