Heat the oven to 375°F and coat a 9-by-13-inch baking dish with cooking spray.
Spread the tortilla pieces, black beans and green chiles evenly in the dish.
Whisk the eggs, milk, cumin and salt in a large measuring cup, then pour the mixture across the tortillas.
Press down dry tortilla corners and scatter the pepper Jack over the top.
Bake uncovered for 38 to 45 minutes, until the center reaches 160°F and no liquid egg runs into a small cut at the center.
Rest for 10 minutes before cutting into squares.