In a large Dutch oven or stockpot, add chicken stock and heat over medium heat. Add chicken breasts, cumin, chili powder, and cayenne pepper. Simmer about 20-25 minutes until chicken is cooked through. Remove chicken and set aside. Add tomatoes, jalapenos, bell pepper, onion, and garlic to the pot. Simmer about 30 minutes, covered until tomatoes have begun to break down. Add black beans, corn, and tomato paste and stir to incorporate. Add cotija cheese and half of the pepperjack cheese and stir to melt. Return chicken to soup and cook about 20 more minutes until desired consistency.
If soup isn't as thick as desired, you can add strips of flour tortillas. They will dissolve into the soup to thicken the broth. Add cilantro, reserving some to top individual bowls if desired. Ladle into serving bowls and top with crushed tortilla chips, reserved pepperjack cheese and cilantro if desired.