Place a rack in the upper third of the oven (usually the second-most slot from the top) and preheat the oven to broil.
In a medium ovenproof skillet, heat the oil over medium-high heat until hot but not yet smoking. Add the bell pepper, onion, poblano, and jalapeño. Cook, stirring occasionally, until the vegetables are softened, about 8 to 9 minutes.
Add the garlic, chili powder, cumin, and salt and stir constantly. Continue cooking and stirring until fragrant, about 1 minute.
Sprinkle the flour over the vegetables and cook, still stirring constantly, until they are thoroughly coated and the white bits of flour disappear, about 1 minute.
Stir in the broth and bring to a boil. Stir and cook until the mixture is somewhat thickened, about 3 minutes. Reduce the heat to low.
Break the cream cheese into the skillet in bits. Stir until melted. Gently stir in the chicken, diced tomatoes, torn tortillas, and half of the cheese. Sprinkle the remaining cheese over the top.
Place the skillet under the broiler. Broil until the cheese is melted and browned, about 1 to 2 minutes. Do not walk away. Watch the skillet the entire time to make sure it doesn’t burn.
Sprinkle with cilantro. Serve hot with a dollop of Greek yogurt.
