Preheat your oven to 350°F (175°C).

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

Grease an 8x8 or 9x9 baking dish. Layer half of the roasted green chiles evenly across the bottom.

Sprinkle half of the shredded Monterey Jack cheese over the layer of chiles.

Pour half of the prepared egg mixture over the layered chiles and cheese.

Add the remaining roasted green chiles on top of the first layer, followed by the rest of the Monterey Jack cheese.

Pour the remaining egg mixture over the final layer of cheese and chiles.

Place the baking dish in the preheated oven and bake for 35 minutes until golden and a knife inserted comes out clean.

Remove from the oven and let cool for about 5-10 minutes before serving.