Preheat the broiler. Line a small baking sheet with aluminum foil and arrange the tomatoes in a single layer on top. Broil for 8 to 10 minutes, flipping halfway through, until the skin is blackened and blistered. Set aside.
Carefully toast the pasilla peppers over an open flame for a few seconds on each side until very fragrant. Alternatively, toast the peppers in a small skillet over medium-high heat for 10 to 20 seconds, until fragrant. Be careful not to burn the peppers. Set aside.
Heat the oil in a large pot or Dutch oven. Add the onion and garlic and saute for 10 minutes, stirring occasionally, until softened.
Add the cooked onion, garlic, toasted peppers, and roasted tomatoes to a large blender. Blend until completely smooth.
Heat the remaining 2 tablespoons of oil in the same large pot of Dutch oven. Pour in the blended tomato mixture and cook for 5 minutes, stirring occasionally.
Add the chicken breast, broth, and salt. Raise heat to high and bring to a boil, reduce heat to low, cover, and simmer for 15 minutes, or until chicken is tender and cooked through.
While the soup is cooking, make the tortilla strips by heating ¼ cup vegetable oil in a large skillet over medium-high heat. When hot, add in a handful of the tortilla strips and fry for about 60 to 90 seconds, or until golden brown and crispy. Transfer them to a plate lined with paper towels and repeat until all the tortilla strips are fried. Set aside.
Remove the cooked chicken from the pot and transfer to a plate. Shred with 2 forks.
Add the shredded chicken back to the pot along with the black beans and corn. Cook for 3 more minutes.
Remove the pot from the heat and stir in the lime juice. Serve in bowls topped with tortilla strips, queso fresco, avocado, cilantro, and more lime wedges.
Tomatoes: If you don't have fresh tomatoes on hand, you can use 1 ½ cans (about 22 ounces) of fire-roasted diced tomatoes instead.
Chicken: You can use chicken thighs (bone-in or boneless) for an even better flavor. The chicken would be a little juicier and the broth would be extra flavorful thanks to the bones. You could also use shredded rotisserie chicken to save you some time!