Preheat oven to 375 degrees F (190 degrees C). Spray a dark baking sheet with cooking spray.
Mix egg, water, and pepper together in a bowl. Combine bread crumbs, Parmesan cheese, parsley, garlic powder, and onion powder in a separate bowl.
Dip zucchini sticks in egg mixture, allowing excess liquid to drip back into the bowl. Press coated sticks into the bread crumb mixture until fully coated. Arrange coated sticks on the prepared baking sheet in a single layer. Spray sticks with cooking spray.
Bake in the preheated oven for 15 minutes. Carefully flip sticks, trying not to break the coating from the zucchini, and continue baking until lightly browned, about 10 minutes more. If not brown enough, turn on the oven's broiler and broil for 2 to 3 minutes.