Sauté the aromatics: Heat olive oil in a large pot over medium heat. Add onion, bell pepper, and celery.
Cook 5 to 6 minutes, stirring, until softened.
Build the flavor base: Stir in garlic and jalapeño. Cook 30 to 60 seconds until fragrant. Add cumin, oregano, coriander (if using), smoked paprika, and the bay leaf.
Toast the spices for 30 seconds to wake them up.
Add liquids and veggies: Pour in the chicken broth and tomatoes with their juices. Stir in corn and black beans. Bring to a gentle boil.
Cook the chicken: Nestle the whole chicken breasts into the pot.
Reduce heat to a steady simmer. Cover and cook 12 to 16 minutes, or until the chicken reaches 165°F in the thickest part.
Shred and return: Transfer chicken to a cutting board and shred with two forks. Return shredded chicken to the pot.
Season and brighten: Add lime juice and cilantro.
Taste and season with salt and pepper. If the soup needs more depth, add another pinch of cumin or a splash of broth.
Serve: Ladle into bowls and top with avocado, baked tortilla strips, extra cilantro, and lime wedges as you like.