Butter a 9-by-13-inch baking dish and arrange half the croissant pieces across the bottom.
Scatter on the ham and 1 1/2 cups Swiss, then cover with the remaining croissant pieces.
Whisk the eggs, milk, Dijon, salt, pepper and onion powder. Pour evenly into the dish and press the bread gently into the custard. Sprinkle with the remaining cheese.
Cover and refrigerate for 8 to 14 hours. Let the dish stand out for 30 minutes and heat the oven to 350°F.
Bake uncovered for 45 to 50 minutes, until the center is set at 160°F and the top is golden. Rest 10 minutes before serving.