Rinse the whole roasted green chiles under cold water and gently pat them dry. Slice them open lengthwise to remove seeds and set aside. Preheat the oven to 350°F (175°C).

Cut the Monterey Jack cheese into evenly sized sticks or cubes.

In a large mixing bowl, whisk together the large eggs, all-purpose flour, kosher salt, and milk until smooth.

Gently fold the rinsed chiles and cheese sticks into the egg mixture.

Pour the mixture into a greased 9x13-inch baking dish, spreading it evenly.

Sprinkle additional grated cheese on top of the casserole mixture.

Bake for 25-30 minutes until the top is bubbly and golden brown.