Butter a 9-by-13-inch baking dish. Arrange the cornbread cubes in the dish and scatter the drained chiles and pepper Jack between them.
Whisk the eggs, milk, cumin, salt, garlic powder and pepper until smooth.
Pour the custard over the cornbread. Press lightly once, taking care not to mash the cubes.
Cover and refrigerate for at least 8 hours and up to 14 hours. Let stand at room temperature for 30 minutes while the oven heats to 350°F.
Bake uncovered for 45 to 50 minutes, until lightly browned and 160°F in the center. Rest 10 minutes before cutting.