Heat the oven to 350°F and butter a 9-by-13-inch baking dish with 1 teaspoon of the butter.
Melt the remaining butter in a skillet over medium heat and cook the onion and bell pepper for 7 to 9 minutes, until soft but not browned.
Stir in the soup, tomatoes with green chiles, broth, chili powder and cumin, and heat until the sauce just begins to bubble.
Layer half the tortilla pieces, half the chicken, half the sauce and half the cheddar in the dish, then repeat the layers.
Cover with foil and bake for 25 minutes.
Uncover and bake for 15 to 20 minutes more, until the center is bubbling and reaches 165°F, then rest for 10 minutes before scooping.