Heat oven to 350°F. In 12-inch skillet, heat oil over medium-high heat. Add onions; cook 20 to 25 minutes, stirring occasionally, until onions are brown and caramelized.
Meanwhile, spray 13x9-inch (3-quart) glass baking dish with cooking spray. Layer 4 cups of the bread cubes, 1 1/2 cups of the zucchini and 3/4 cup of the cheese in baking dish. Repeat layers once.
In large bowl, beat remaining ingredients with wire whisk until well blended. Pour over bread mixture. Arrange onions on bread mixture.
Cover with foil; bake 30 to 40 minutes or until knife inserted in center comes out clean. Sprinkle remaining 1/2 cup cheese over top; bake 2 to 3 minutes longer or until cheese is melted.