Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper. Stack tortillas, slice into thin strips about ¼ inch wide and 2-3 inches long, toss with oil and salt, and bake for 12-15 minutes, flipping halfway, until golden and crispy. Set aside.
Heat olive oil in a large Dutch oven or soup pot over medium-high heat. Add diced onion and jalapeño and cook for 4-5 minutes until soft and translucent. Add minced garlic and cook for 30-60 seconds until fragrant.
Sprinkle in cumin, chili powder, smoked paprika, garlic powder, and cayenne (if using). Stir and cook for 1 minute, stirring constantly, to toast and bloom the spices.
Pour in both cans of diced tomatoes with their juices, then add the black beans, corn, and chicken broth. Stir to combine and season with salt and pepper to taste.
Nestle the raw chicken breasts into the pot, fully submerged in broth. Bring to a boil, then reduce heat to medium-low, cover, and simmer for 20-25 minutes until chicken reaches 165°F (74°C).
Using tongs, transfer the cooked chicken to a cutting board and let rest for 2-3 minutes. Shred with two forks, then return the shredded chicken to the pot and stir.
Stir in the fresh lime juice and chopped cilantro. Simmer for 3-5 minutes on low to meld the flavors. Adjust salt, pepper, or lime juice to taste.
Ladle the soup into bowls. Top with crispy tortilla strips, diced avocado, shredded cheese, sour cream, extra cilantro, and lime wedges on the side. Serve immediately.