Add olive oil to the Instant Pot. Using the display panel select the SAUTE function.
When oil gets hot, add onion to the pot and saute until soft, 3-4 minutes. Add garlic and cook for 1-2 minutes more.
Add broth to the pot and deglaze by using a wooden spoon to scrape the brown bits from the bottom of the pot.
Add chicken, beans, chiles, chili powder, salt and pepper and stir to combine.
Turn the pot off by selecting CANCEL, then secure the lid, making sure the vent is closed.
Using the display panel select the MANUAL or PRESSURE COOK function*. Use the +/- keys and program the Instant Pot for 15 minutes.
When the time is up, let the pressure naturally release for 10 minutes, then quick-release the remaining pressure.
Carefully remove the chicken from the pot to a cutting board and shred, then return to the pot.
In a medium bowl, melt butter, then whisk in flour until well combined. Stir into the pot and simmer 3-5 minutes until thickened, returning to SAUTE mode as needed.
Stir in warmed milk, sour cream and lime juice. Adjust seasonings.
Serve hot topped with cilantro and shredded cheese (optional).