Press the saute button on Instant pot. Add vegetable oil and heat until hot. Add the onion and poblano and cook 4-5 minutes, until soft. Add garlic and cook until fragrant, about 30 seconds.
Add chili powder, cumin, chicken base (if using), salt, pepper, paprika, and oregano and stir.
Add can of undrained tomatoes and stir using a wooden spoon to scrape the bottom of the pot to ensure no browned bits are stuck on there.
Add in can of drained black beans and can of drained corn, then pour in chicken broth.
Place chicken breasts into the liquid, then cancel the saute function, and secure Instant Pot lid, making sure the valve is set to "sealing". Press the Pressure Cook or Manual button and use the +/- buttons to set the timer for 12 minutes.
Once the timer beeps, let out the pressure by carefully moving the valve to “venting" to perform a quick release.
When the pin drops, remove lid and set aside. Press the saute button once again, and add heavy cream and lime juice. Stir and heat for just a minute or two, until cream is warmed through.
Press Cancel and unplug the Instant Pot. Serve soup hot, topped with desired toppings.