Place the broccoli florets and 1 tablespoon water in a 1-quart microwave-safe casserole dish. Cover with vented plastic wrap, and microwave on 100 percent power (high) for 2 to 3 minutes or until just tender; drain well. Or, cook broccoli, covered, in a small amount of boiling water for 4 to 6 minutes or until just tender; drain well. Set aside.
Layer half of the bread cubes in a greased 2-quart square baking dish. Top with cheese, ham, and broccoli. Top with the remaining bread cubes. In a mixing bowl, combine the beaten eggs, milk, onion, mustard, and pepper. Pour egg mixture evenly over the layers in dish. Cover and chill in the refrigerator for 2 to 24 hours.
Uncover and bake in a 325 degree F. oven for 1 hour or until a knife inserted near the center comes out clean. Let stand about 5 minutes before serving. (Pictured with the strata are Orange-Cherry Twists.) Makes 6 servings.