Heat the oven to 350 F. Lightly coat a 9-inch square baking dish with cooking spray.
In a nonstick skillet, combine the broccoli, onion and water. Saute over medium-high heat until the vegetables are tender, about 5 to 8 minutes. Keep adding water to prevent the vegetables from drying out, but use as little water as possible. Drain and set aside when the broccoli is done.
In a bowl, combine the egg substitute, milk and 3/4 cup cheese. Add in the broccoli mixture and pepper. Stir to mix well.
Transfer the mixture into the prepared baking dish. Set the baking dish into a large pan filled with about 1 inch of water. Bake uncovered until a knife inserted in the center comes out clean, about 45 minutes. Remove from the oven and top with the remaining 1/4 cup shredded cheese. Let stand about 10 minutes before serving.