Trim zucchini-cut crosswise in half, then cut each piece into 1/4 inch sticks. Add cheese to coating mix in shaker bag; shake gently to combine.
Whisk egg in medium bowl.
Add zucchini; toss to coat. Use tongs to place 1/4 of the zucchini in bag, close bag, toss to coat evenly. Spread on baking sheet coated with cooking spray. Repeat with remaining zucchini.
Bake for 12-13 minutes, rotating baking sheet after 7 minutes, until zucchini are golden brown, and evenly cooked.