Preheat oven to 180ºC (175 degrees C). Grease an 8x12 inch baking dish.
Line the bottom of dish with green chiles. Sprinkle with half cup shredded cheese. Repeat layers twice more. In a medium bowl, whisk together milk and eggs. Season with salt and pepper. Pour egg mixture over chiles and cheese.
Bake in preheated oven for 25 to 30 minutes, or until filling is set. Let stand 5 to 10 minutes before serving.