Preheat the oven to 350°F and grease an 8x8-inch baking dish.

In a medium bowl, whisk together the eggs, evaporated milk, flour, and salt until well-combined.

Spread half of the green chiles in an even layer on the bottom of the prepared dish, then top with half of the shredded cheese. Top with the remaining chiles and then the remaining shredded cheese. Pour the custard over the casserole.

Bake until puffed, the top is golden-brown, and the center is set, about 45 to 55 minutes. Remove from the oven and allow to cool for 10 minutes before serving.

Refrigerate cooled leftovers in an airtight container for up to 4 days. Reheat in the microwave or a 350°F oven until warmed through.