Place the chicken breasts in the bottom of the Instant Pot insert in a single layer. Add the drained beans, green chiles, diced onion, minced garlic, and chicken broth on top. Sprinkle in the cumin, garlic powder, oregano, chili powder, and salt. Stir gently to combine everything around the chicken.

Lock the lid and set the valve to Sealing. Select Pressure Cook or Manual on High and set the timer for 18 minutes. The pot will take about 10 to 12 minutes to come to pressure before counting down.

When the cook time ends, switch the valve to Venting for a quick pressure release. Stand back from the steam and keep your hand clear of the vent. Once the pin drops and all steam has escaped, carefully open the lid.

Use two forks to shred the chicken directly in the pot. It should pull apart easily. Stir everything together so the shredded chicken mixes into the broth and beans.

Add the softened cream cheese chunks to the hot chili. Stir steadily for about 2 minutes until the cream cheese fully melts into the broth and you no longer see white pieces. If you want extra creaminess, stir in the sour cream at this point too.

Taste and adjust salt as needed. Ladle into bowls and top with shredded pepper jack cheese and a handful of tortilla chips. Sliced jalapenos or a squeeze of lime juice are great additions if you have them on hand.