Position 1 oven rack 8 inches from broiler and 1 oven rack to middle position; preheat oven to 425°. Spray rimmed baking pan and 8½ x 11-inch baking dish with cooking spray. Toss broccoli, cauliflower and carrots on prepared pan; spray with cooking spray, and sprinkle with ½ teaspoon each salt and pepper. Roast broccoli mixture on middle rack 15 minutes or until almost tender; spread in prepared dish.
In medium bowl, whisk egg; stir in cheeses, garlic powder, chives, and remaining ¼ teaspoon each salt and pepper. Spread over broccoli mixture; bake 10 minutes or until vegetables are tender-crisp. Turn broiler to high; broil 3 minutes or until top is golden brown. Serve garnished with chives, if desired, Makes about 8 cups.