Special equipment: 2 wire racks 2 rimmed baking sheets
Adjust 2 oven racks to the top and bottom thirds of the oven and preheat to 425 degrees F. Put the wire racks in the baking sheets and coat each generously with cooking spray.
Combine the flour and 3/4 teaspoon salt in a large re-sealable plastic bag. Combine the eggs and 3/4 teaspoon salt in another large plastic bag; combine the breadcrumbs, Parmesan and 3/4 teaspoon salt in a third large plastic bag.
Add about a half of the zucchini sticks to the bag with the flour and use a combination of your hands and shaking the bag to coat the zucchini. Remove the zucchini and shake off any excess flour. Transfer to the egg wash and repeat until coated. (It's less messy if you use only one hand for the dry ingredients and the other for the wet.) Let any excess egg drip off before transferring to the breadcrumb mixture; repeat until fully coated (you'll still see some green and white of the zucchini peeking through the breading). Transfer to the prepared baking sheets and coat the breaded zucchini generously with cooking spray (there's no need to turn them). Repeat with the remaining zucchini.
Bake, rotating the baking sheets from top to bottom about halfway through, until golden brown and tender, 25 to 30 minutes. Sprinkle with a little salt and serve warm with your favorite dipping sauces.
Some panko breadcrumbs are coarser then others. Rub the breadcrumbs between your fingers to make them finer, which will help them coat the zucchini pieces better.
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