Before you begin assembling the rest of your ingredients, start cooking the chicken breasts. Generously salt and pepper both sides of the chicken.
In a large pot with a lid, heat 1 tablespoon of the oil over medium-high heat. Add the chicken and cook undisturbed until well-browned, 2 to 4 minutes, flip and repeat. Once both sides are browned, add filtered water to the pot until it comes about halfway up the sides of the chicken pieces (it doesn’t need to be exact). Bring the water to a simmer, cover the pot and turn the heat down to medium.
Cook for 8 to 15 minutes, until the chicken is cooked through and an instant-read thermometer inserted into the center of the meat reads 165°F (170°F if you’re going to shred the chicken). Check occasionally and add more water if the majority has evaporated. (Do not allow all the water to evaporate!) Larger chicken breasts will take longer to cook, so be sure to check for doneness before removing from heat.
While your chicken cooks, prep the rest of your ingredients for the soup. Once the chicken is cooked through, transfer it and any liquid left in the pot to a clean plate or bowl.
Return the pot to the stove and add the remaining 1 tablespoon of olive oil. Heat over medium heat and add the onions and minced garlic. Cook for 3 to 5 minutes, until the edges of the onions begin to turn translucent, stirring well to remove any cooked on bits of chicken stuck to the bottom of the pot. Stir in the chili powder, cumin, paprika, and oregano, and cook for 1 minute.
Stir in the tomato paste and cook, stirring often, until the tomato paste just begins to stick to the bottom of the pot, 30 seconds to 1 minute. Stir in the chicken broth, pinto and black beans, diced tomatoes, and green chilis. Simmer for 15 minutes.
Add corn and simmer for 5 minutes more. While the soup cooks, dice or shred the cooked chicken breast and add it into the soup.
Taste and add salt and pepper as needed. Stir in the cream or sour cream and then check salt levels once more. Serve topped with cheese and cilantro if desired, and enjoy!