Add ½ cup chicken broth and chicken thighs to the Instant Pot. Close the lid, seal the valve, and cook on manual pressure for 8 minutes. Once done, allow a natural release for 5 minutes, then release the remaining pressure manually.
Check that the internal temperature of the chicken has reached 165°F using a meat thermometer. Remove the chicken, shred with two forks, and set aside.
To the Instant Pot, add the remaining 2 cups of chicken broth, ranch seasoning, fire roasted tomatoes (with juices), egg noodles, cubed cream cheese, and milk. Gently stir everything together.
Seal the lid again and cook on manual pressure for 3 minutes. Let the pressure naturally release for at least 10 minutes before opening the lid.
Stir everything well until the cream cheese has melted and the sauce is smooth and creamy.
Stir in the parmesan cheese until fully melted and combined.
Return the shredded chicken to the pot and stir to coat everything evenly.
Taste and season with salt and black pepper as needed.
Serve warm with optional toppings like chopped chives, extra parmesan, or crispy bacon.