Position oven racks in the upper third and center of the oven and preheat to 425°F (220°C).
Heat the olive oil in a large oven-safe skillet over medium heat until hot.
Add the diced onion, red bell pepper, and poblano (or green bell pepper) to the skillet along with the garlic powder, cumin, dried oregano, kosher salt, and black pepper; sauté until the vegetables are browned and becoming tender, about 6 minutes.
Remove the skillet from the heat and transfer the sautéed vegetables to a large mixing bowl.
To the bowl, add the enchilada sauce, shredded chicken, rinsed and drained beans, and Greek yogurt; stir until combined.
Fold in the tortilla quarters and 1/4 cup of the shredded cheese so the pieces are coated and distributed evenly.
Spoon the mixture back into the same skillet and sprinkle the remaining cheese evenly over the top.
Bake on the upper third rack until the cheese is hot and bubbling, about 10 minutes; optionally broil 1–2 minutes to brown the top, watching carefully to avoid burning.
Remove from the oven with oven mitts, let rest a few minutes, then serve hot with diced avocado, sliced jalapeño, chopped cilantro, and extra Greek yogurt or sour cream if desired.
