In a large saucepan or dutch oven over medium-high heat, add 2 tablespoon oil and heat until hot and shimmering. Add tortilla strips and fry until golden, about 4 minutes total. Remove strips to a towel lined plate to drain and set aside.
Reduce heat to medium and add chicken breasts to remaining oil, adding additional oil if necessary after the tortillas are fried. Cook chicken without disturbing until browned on one side, about 2 minutes, then flip and continue browning on other side, approximately another 2 minutes. Remove chicken and set aside.
Add remaining 2 tablespoons oil, onion, garlic, chili powder and cumin to the pan over medium heat. Stir to coat onions with the flavorful spices and cook aromatics until soft, about 3 minutes.
Then stir in tomato puree and cook slightly, about 1 minute, before adding the chicken stock. Once tomato sauce is thickened slightly stir in chicken broth and add chicken breasts back to the liquid along with any accumulated juices.
Bring to a simmer and cook until chicken reaches 165 degrees Fahrenheit, about 5-10 minutes. Remove chicken all allow to cool, then shred with two forks or cut into slices.
Add the juice of 1 lime to the broth and season to taste with salt and pepper.
Place shredded chicken in bowl and ladle over the flavorful tortilla soup broth then top with crispy tortilla strips and any other desired tortilla soup toppings.