Place a rack in the upper third of the oven (usually the second-most slot from the top) and preheat the oven to broil.: The oven should already be warming so the top of the casserole browns quickly once it goes under the heat. You will notice the kitchen warming and the light inside the oven becoming steady, which signals readiness. Proper rack placement ensures even browning on top without burning the middle. A common misstep is placing the rack too close to the broiler, which can char the cheese before the casserole heats through.
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.: As you saute, listen for a steady sizzle and watch the vegetables go from shiny and firm to softened and slightly translucent, with edges taking on a touch of brown. The smell will shift from raw vegetal to sweet and roasted, which is crucial for depth. Stir occasionally to ensure even cooking. If you rush with overly high heat, the outsides will brown but the insides may remain raw, so moderate heat and patience are key.
Add the garlic, chili powder, cumin, and salt and stir constantly. Continue cooking and stirring until fragrant, about 1 minute.: As the spices toast briefly, they will bloom and release a perfume that lifts the whole dish, and the garlic will take on a mellow, nutty scent. Stirring keeps the tiny garlic pieces from sticking and burning, which would impart bitterness. Watch closely because spices and garlic can go from fragrant to burnt in seconds.
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.: The flour should form a thin paste with the vegetable juices, losing its raw powdery appearance and beginning to sizzle gently. This step is the base for thickening; cook just long enough to remove raw taste. Under-cooking leaves a pasty mouthfeel, while overcooking can darken the roux and alter flavor.
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.: When the broth hits the skillet it should bubble lightly and start to thicken as the flour activates; you will see the sauce coat the back of a spoon. Reducing to low prevents separation and helps the sauce become smooth and glossy. A mistake is boiling too vigorously which can thin the sauce by evaporating liquid unevenly.
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.: The cream cheese will melt into a silky, slightly tangy base, making the sauce cling to the torn corn tortillas . As you fold in the chicken and tomatoes, listen for a low bubbling and see the mixture come together into a cohesive, thickened casserole. Stir gently to avoid breaking up the chicken too much. Adding cold cream cheese can create lumps, so bringing it to room temperature helps it incorporate smoothly.
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.: The reserved cheese layer is what browns and becomes golden under the broiler, giving the casserole a rich finish. Evenly distribute the cheese so it melts uniformly, creating a single bubbly sheet. Piling cheese too high can lead to uneven browning and a greasy top, so keep it moderate.
Sprinkle with cilantro. Serve hot with a dollop of Greek yogurt.: In these moments the casserole will go from melty to blistered and browned, releasing a toasty, savory aroma. Watch constantly, and keep the oven door cracked if your broiler tends to be intense, so you can see the color develop. Stepping away leads to burnt cheese in the blink of an eye, so remain attentive.
Sprinkle with cilantro and serve hot with a dollop of Greek yogurt: Fresh cilantro adds a bright, herbal finish and the Greek yogurt adds a cool, tangy contrast that balances the spices. Spoon portions onto warm plates and add yogurt at the end so its texture stays creamy. Adding yogurt before reheating can cause it to separate, so reserve it for serving.