Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook for 5-7 minutes, stirring occasionally, until the onion is soft and translucent.
Add the minced garlic, cumin, and chili powder to the pot and cook for 1 minute, stirring constantly, until the spices are fragrant.
Place the whole chicken breasts into the pot. Pour in the chicken broth and green enchilada sauce. Bring the liquid to a boil, then reduce the heat to low, cover, and simmer for 15-20 minutes, or until the chicken is cooked through and easily shreds with a fork.
Remove the chicken from the pot and place it on a cutting board. Use two forks to shred the chicken into bite-sized pieces, then return it to the soup.
Stir in the diced green chiles, black beans, and frozen corn. Bring the soup back to a simmer and cook for 5 minutes to heat everything through.
Turn off the heat. Stir in the heavy cream and sour cream until the soup is smooth and creamy. Season with the salt and pepper, tasting and adjusting as needed.
Ladle the hot soup into bowls and top with shredded cheese, tortilla strips, a dollop of sour cream, and fresh cilantro.