In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent. Stir in the minced garlic and cook for an additional minute until fragrant.

Add the diced poblano peppers, cumin, chili powder, and smoked paprika. Cook for another 5 minutes, stirring occasionally.

Pour in the chicken broth and add the diced tomatoes, black beans, shredded chicken, and corn. Season with salt and pepper to taste. Bring the mixture to a simmer and let it cook for 15-20 minutes to allow the flavors to meld.

While the soup is simmering, prepare your toppings. In a small bowl, combine the diced avocado, chopped cilantro, and lime juice.

To serve, ladle the soup into bowls and top with crushed tortilla chips, the avocado-cilantro mixture, and shredded cheese. Serve with lime wedges on the side.