Sauté the Aromatics: In a large pot, heat a tablespoon of olive oil over medium heat. Add the diced onion and cook until softened, about 3-4 minutes. Add the minced garlic and cook for another 30 seconds, making sure not to let the garlic brown too much to avoid bitterness.
Cook the Chicken: Season the chicken breasts with chili powder, cumin, smoked paprika, salt, and pepper. Add the chicken breasts to the pot and sear on both sides for about 5 minutes each, until lightly browned.
Build the Soup Base: Add the enchilada sauce, chicken broth, black beans, and corn. Stir everything together and bring the soup to a simmer. Let it cook for 20 minutes to allow the flavors to blend.
Shred the Chicken: After the chicken has cooked through, remove it from the pot and shred it using two forks. Return the shredded chicken to the pot and stir it into the soup.
Finishing Touches: Add lime juice to the soup to brighten up the flavors. Taste and adjust seasoning as needed. Let the soup simmer for another 5 minutes to meld the flavors.