Sauté the Vegetables: Heat the oil in a large soup pot or Dutch oven over medium-high heat until it starts to shimmer. Add the chopped onion and jalapeños, stirring occasionally, and cook for about 5 minutes, until the vegetables are softened and the onion turns slightly golden. Stir in the minced garlic and cook for an additional minute until fragrant.
Combine the Ingredients: Pour in the chicken broth, crushed tomatoes, and add the chicken breasts, black beans, corn, cumin, chili powder, salt, and pepper. Stir everything together and bring it to a boil. Once boiling, reduce the heat to maintain a gentle simmer. Let it cook uncovered for about 20 minutes, stirring occasionally to prevent sticking.
Shred the Chicken: Use tongs to remove the cooked chicken breasts from the pot and place them in a bowl. Using two forks (or a stand mixer with a paddle attachment), shred the chicken into small pieces. Return the shredded chicken to the soup and simmer for another 5 minutes to allow the flavors to blend.
Add Final Touches: Stir in the chopped cilantro and freshly squeezed lime juice. Taste the soup and adjust the seasoning with additional salt and pepper if needed.
Serve: Ladle the soup into bowls and top with your choice of shredded cheese, diced avocado, tortilla strips or chips, sour cream, and more cilantro.
Storing for Later: If you want to freeze the soup, allow it to cool completely before transferring it to an airtight container. Do not add toppings before freezing. It can be stored in the freezer for up to 3 months.