Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and cook for about 5 minutes until it becomes translucent and soft. Stir in the minced garlic and cook for another minute until fragrant, being careful not to let it burn.
Pour in the chicken broth and the red enchilada sauce. Add the diced tomatoes with green chilies (do not drain them), cumin, chili powder, and salt. Stir everything together and bring the mixture to a gentle boil.
Reduce the heat to low. Stir in the shredded cooked chicken, drained black beans, and drained corn. Let the soup simmer for 15 to 20 minutes. This allows the spices to penetrate the chicken and the flavors to meld together beautifully.
Just before serving, stir in the shredded cheese. Keep stirring until the cheese is completely melted and the soup has a slightly creamy, rich consistency. Taste and adjust the seasoning if necessary.