In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes, until translucent.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the chicken breasts to the pot and pour in the enchilada sauce and chicken broth. Bring to a gentle simmer.
Season with ground cumin, smoked paprika, chili powder, salt, and pepper. Let the soup simmer for about 20-25 minutes, or until the chicken is cooked through.
Once the chicken is cooked, remove it from the pot and shred it using two forks. Return the shredded chicken back to the pot.
Add the black beans and corn to the soup. Stir to combine and let it simmer for another 5-10 minutes, allowing all the flavors to meld together.
Right before serving, stir in the shredded Cheddar cheese until melted.
Serve the soup warm, topped with a dollop of sour cream, a sprinkle of fresh cilantro, and lime wedges on the side for squeezing over the top.