Place the instant pot on sauté mode (medium). Add the butter, ghee or olive oil. Once hot add the chicken breasts and sear for 2 - 3 minutes per side. Turn off sauté. Add the onion, cumin, coriander, oregano, paprika, optional cayenne, salt, pepper, green chiles, jalapeño, garlic, and broth. Stir to combine.
Secure the lid on the instant pot and close the pressure valve. Press the “pressure cook” button and set the time to cook for 20 minutes at high pressure. Once the time is up, quick release the pressure.
When the pressure has released, remove the lid and chicken breasts. Place chicken on a chopping board and shred chicken with two forks.
Switch the Instant Pot back to sauté mode, medium, and set the timer for 15 minutes allowing the broth to concentrate and reduce. Add the heavy cheese and cream cheese (or coconut milk for dairy-free) for the last 3 minutes, whisking it with a hand balloon whisk until combined. Taste and adjust the seasoning. Add the chicken back in and allow to warm through.
Ladle into bowls and serve with desired toppings and cauli rice or veggies.