Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13 inch baking dish.
In a large bowl, whisk together eggs, milk, salt, and pepper. Stir in green chiles and 1/4 cup cheese.
Pour egg mixture into the prepared baking dish. Drizzle melted butter over the top.
Bake in preheated oven for 20 minutes, then sprinkle remaining 1/4 cup cheese over the top. Bake for an additional 5 minutes, or until cheese is melted and eggs are set.
Interesting Facts
Green chiles are a type of pepper native to Mexico.
This dish can be served as a breakfast, lunch, or dinner.
This dish can be made ahead of time and stored in the refrigerator for up to 3 days.