Preheat the oven to 350°F (175°C). Lightly grease a baking dish and set it aside.
Arrange half of the green chiles in an even layer across the bottom of the prepared dish.
Sprinkle half of the shredded Monterey Jack (or Pepper Jack) and cheddar cheeses evenly over the chiles.
Place the remaining green chiles on top, then finish with the rest of the shredded cheese.
In a mixing bowl, whisk together the eggs, milk, heavy cream, flour, baking powder, salt, black pepper, garlic powder, and onion powder until smooth and well combined.
Slowly pour the egg mixture over the layered chiles and cheese, allowing it to settle evenly throughout the dish.
Place the casserole uncovered in the oven and bake for 40–45 minutes, until puffed, lightly golden, and set in the center.
Remove from the oven and let rest for 5–10 minutes before slicing and serving.
