Melt butter in a large soup pot over medium heat.
Add chopped onions, carrots, and celery to the pot and cook 3 minutes. Add jalapenos and garlic and cook for 1 more minute, until fragrant.
Add the chicken broth, tomatoes, whole chicken breasts, corn tortillas, chili powder, paprika, cumin, and salt. Simmer covered for 20 minutes.
Remove the poached chicken breasts from pot and let rest on a cutting board for 5 minutes. Using 2 forks shred chicken and add back to simmering pot.
Add corn, black beans, milk, lime juice, and cilantro. Continue to simmer uncovered for 20 minutes. Stir well and season with additional salt if needed.
Ladle soup into serving bowls and sprinkle with optional toppings like shredded cheese, a dollop of sour cream, avocado slices and chopped fresh cilantro. Serve a wedge of lime and a few corn tortilla chips on the side!