Preheat your oven to 350°F (175°C).
Grease a 9x13-inch baking dish with nonstick spray or butter.
In a bowl, combine the grated Monterey Jack and Cheddar cheeses.
Sprinkle two-thirds of the cheese mixture evenly over the bottom of the prepared baking dish.
In another bowl, mix the flour and baking powder.
Gradually whisk in the milk to form a smooth paste.
Add the eggs, salt, and melted butter, and whisk until thoroughly combined.
Stir the green chiles into the egg mixture.
Pour the entire egg mixture over the cheese layer in the baking dish.
Sprinkle the remaining cheese on top.
Bake in the preheated oven for 35-40 minutes, until the casserole is set and lightly browned on the edges.
Serve warm.