Preheat oven to 400°F.

Heat 3 tablespoons oil in a large ovenproof skillet over medium heat. Add 1 sliced red pepper, 1 sliced yellow pepper and 1 sliced onion; cook, stirring, for 2 minutes. Stir 4 teaspoons chili powder, 2½ teaspoons cumin, 1¼ teaspoons garlic powder, ¾ teaspoon salt and ¼ teaspoon pepper together in a small bowl. Set aside 1 teaspoon spice mixture and sprinkle the remaining spices over the vegetables. Continue cooking and stirring until softened, about 4 minutes more.

Combine 2½ cups cooked sliced chicken and the reserved spice mix in a medium bowl; add to the skillet. Cook, stirring, until the chicken is warmed, about 2 minutes. Remove from heat and stir in 1 tablespoon lime juice. Gently stir in 6 tortillas cut into strips. Sprinkle with 1 cup cheese. Transfer to the oven and bake until the casserole is hot and the cheese is melted, 15 to 20 minutes. Sprinkle with ¼ cup cilantro.