HEAT oven to 450ºF.
CUT zucchini crosswise in half, then cut each piece into 1/4-inch-thick matchlike sticks. Add cheese to coating mix in shaker bag; shake gently to combine. Whisk egg in medium bowl.
ADD zucchini, in batches, to egg; toss to coat. Use tongs to add 1/4 of the zucchini to coating mix in shaker bag; close bag, then shake to evenly coat zucchini. Spread onto rimmed baking sheet sprayed with cooking spray. Repeat with remaining zucchini.
BAKE 12 to 13 min. or until golden brown, turning after 7 min. Serve with dressing.