Preheat the oven to 375°F (190°C). Lightly slick a 13-by-9-inch (33-by-23 cm) baking dish with butter or oil.
Melt the butter or heat the oil in a large skillet over medium-high heat. Add the onion and the bell pepper, poblano pepper, and jalapeño peppers and cook, stirring frequently, until tender and lightly browned, 8 to 10 minutes.
Add the garlic, chili powder, cumin, salt, and pepper, and cook, stirring, for 1 minute.
Sprinkle the flour over the vegetable mixture and cook, stirring constantly, for 1 minute. Still stirring constantly, slowly stir or whisk in the stock and bring to a boil. Boil until the mixture thickens, which could take anywhere from 1 to 2 minutes. Remove from the heat.
Add the tomatoes and sour cream to the skillet and stir to combine. Add the chicken and cilantro and stir again until blended.
Combine the cheeses in a small bowl.
Place a large cast-iron skillet or wok over medium-high heat. Lightly brush each tortilla on both sides with oil. Cook the tortillas, working with just a couple at a time, on the hot skillet or wok until lightly browned and crisp, flipping once, about ‘timer minutes=1]1 minutes per side[/timer].
Cover the bottom of the prepared baking dish with 6 tortillas, overlapping the tortillas slightly. Top with 1/2 of the chicken mixture and 1/3 of the cheese mixture. Repeat the layers once, adding 6 more tortillas and the remaining chicken mixture and 1/2 the remaining cheeses. Top with the remaining tortillas and cheese.
Lightly coat a sheet of aluminum foil with butter or oil and cover the baking dish, butter or oil side down. Bake the casserole for 20 minutes.
Uncover the casserole and continue to bake until bubbly and lightly browned on top, 10 to 15 more minutes.
Let the casserole stand 10 minutes to cool slightly and then sprinkle with cilantro, serve, and prepare to be serenaded by compliments.