Preheat the oven to 350 degrees F (175 degrees C).
Spray a 2-quart casserole dish with cooking spray.
Arrange hash brown potatoes evenly in the bottom of the prepared dish. Sprinkle with pepper Jack cheese, then ham, and finally green onions.
Whisk evaporated milk, eggs, pepper, and salt together in a medium bowl. Pour egg mixture over the layers in the dish.
Bake in the preheated oven until a knife inserted in the center comes out clean, 40 to 45 minutes.
Remove from the oven and let stand 5 minutes before serving.
