Preheat the oven to 400 degrees and line two baking sheets with parchment.
Slice the zucchini into four sticks (lengthwise), then each piece again lengthwise into smaller sticks.
Combine the flour, salt, garlic, powder, and black pepper in a gallon sized, zip-lock bag. Add about half of the zucchini strips. Coat them by shaking the bag. Transfer to a plate and repeat with the remaining zucchini sticks.
Whisk the eggs and water together in a shallow dish.
Combine the panko crumbs and Parmesan cheese in a shallow plate.
Dredge the zucchini sticks in the egg mixture and coat throughly, then dredge them in the panko mixture.
Transfer to the baking sheets as you finish dredging, lightly add salt and pepper over the sticks (to taste), and lightly spray tops with cooking spray.
Bake for 20 minutes or until the coating is lightly browned, then turn the broiler on and roast for about 3 minutes more or until crisp and golden brown.