Heat the Instant Pot using the Sauté function. Add the olive oil, diced onion, and diced poblano. Cook, stirring occasionally until the onions are soft and translucent-- about 4 minutes.
Next add the garlic, chili powder, cumin, paprika, and oregano. Stir and cook for an additional minute.
Add the chicken broth, roasted tomatoes, black beans, and chicken breasts. Stir gently.
Attach the lid and ensure the valve is in the sealing position. Set the Instant Pot to Pressure Cook- Manual for 12 minutes.
Once the Instant Pot has finished cooking, allow the pressure to release naturally for 5 minutes. Then, turn the valve to the “venting position” to release any additional pressure.
Remove the chicken and shred or slice it. Return it to the pot and stir to combine.
Serve the soup, garnished with your choice of toppings. Store any leftover soup in an airtight container in the fridge for up to three days.