Preheat oven to 350°F and grease a 9x13-inch baking dish.
Heat olive oil in a large skillet over medium heat. Add diced onion and both bell peppers, cooking until softened, about 5-7 minutes.
In a large bowl, combine both soups, diced tomatoes with green chilies, chicken broth, chili powder, cumin, garlic powder, and the sautéed vegetables. Mix well and season with salt and pepper.
Spread one-third of the torn tortilla pieces in the bottom of the prepared baking dish.
Layer with half of the shredded chicken, then pour one-third of the soup mixture over the chicken. Sprinkle with 1 cup of shredded cheese.
Repeat layers: another third of tortillas, remaining chicken, another third of soup mixture, and 1 cup of cheese.
Top with remaining tortilla pieces, pour remaining soup mixture over all, and finish with the final 1 cup of cheese, spreading to cover completely.
Bake for 35-40 minutes until bubbly throughout and the cheese on top is golden and melted. Let stand 5 minutes before serving.