- 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.