Preheat oven to 350°F. Spread tortillas in a single layer on a baking sheet. Bake until lightly browned and crisp, 10 to 12 minutes.
Meanwhile, heat oil in a Dutch oven over medium-high heat. Add chicken and cook, stirring occasionally, until beginning to brown, 3 to 4 minutes. Transfer to a plate using a slotted spoon. Add pepper-onion mix and cumin to the pot. Cook, stirring occasionally, until the onions are lightly browned, about 4 minutes. Add broth, tomatoes, pepper and lime juice; bring to a simmer and cook, stirring often, until the vegetables are tender, about 3 minutes more. Return the chicken and any accumulated juice to the pot and cook, stirring, until heated through, about 1 minute. Remove from the heat; stir in cilantro. Serve topped with the toasted tortilla strips and cheese.