Preheat oven broiler. Place poblano peppers on a baking sheet. Broil for 5-7 minutes per side, turning with tongs, until skins are blistered and charred.

Transfer peppers to a bowl, cover tightly with plastic wrap, and let steam for 10-15 minutes. Once cooled, peel off the skins, remove stems and seeds, and slice the peppers into strips. Set aside.

While peppers cool, heat 1 tbsp olive oil in a large skillet over medium-high heat. Add cubed chicken seasoned with chili powder, cumin, garlic powder, salt, and pepper. Cook for 5-7 minutes, stirring occasionally, until chicken is cooked through and lightly browned. Remove from skillet and set aside.

In the same skillet (no need to clean), heat 2 tbsp olive oil over medium heat. Add chopped yellow onion and cook for 5-7 minutes until softened and translucent. Add minced garlic and cook for 1 minute more until fragrant.

Stir in crushed tomatoes, chicken broth, oregano, cumin, salt, and pepper. Bring to a simmer, then reduce heat to low and let it cook gently for 10-15 minutes, allowing flavors to meld. Stir in fresh cilantro.

In a medium mixing bowl, whisk together eggs, milk, flour, and a pinch of salt until well combined and smooth. This will form the custard-like base.

Preheat oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish. Spread about 1/2 cup of the tomato sauce on the bottom of the baking dish. Arrange half of the roasted poblano strips over the sauce. Top with half of the cooked chicken. Sprinkle with 1.5 cups of the shredded cheese mixture (Monterey Jack and Colby Jack combined).

Pour about half of the egg mixture evenly over the cheese layer. Repeat the layers: remaining poblano strips, remaining chicken, and remaining shredded cheese (reserving about 1/2 cup for the very top).

Pour the remaining egg mixture over the layers. Gently pour the remaining tomato sauce evenly over the top. Sprinkle with the reserved 1/2 cup of shredded cheese.

Bake for 35-45 minutes, or until the casserole is bubbly, the cheese is melted and golden, and a knife inserted into the center comes out clean (indicating the egg mixture is set).

Remove from oven and let the casserole rest for 10-15 minutes before serving. This allows it to set properly and makes for easier slicing. Serve hot with optional toppings like sour cream, extra cilantro, or sliced avocado.