Using a vegetable peeler or sharp knife, shave or cut the seeds from the inner portion of each zucchini quarter. Halve each quarter lengthwise, then cut in half crosswise.
Preheat the oven to 450°F. Line 2 rimmed baking sheets with parchment paper; set aside. Arrange zucchini in an even layer on a paper towel-lined plate and pat dry. Set aside.
In a food processor, pulse panko until finely ground, 3 to 4 pulses. Transfer to a shallow bowl with Parmesan, oil, and 1 tsp of the salt. Use fingers to toss until panko is completely coated in oil.

In a shallow bowl, add egg whites and lightly beat until frothy. In a separate shallow bowl add flour. Working in 3 batches, dip the zucchini sticks in flour, dusting off excess, then dip into egg whites, allowing excess to drip back into the dish, then transfer into the prepared panko mixture. Turn and press the panko into the zucchini to ensure an even layer on all sides. Divide prepared zucchini fries on the 2 prepared baking sheets, spacing them out at least 1/2 inch apart.

Bake until zucchini is starting to brown, about 12 minutes. Gently flip zucchini, then return to the oven, switching baking sheets top to bottom and rotating front to back, and continue to bake until evenly browned and crisp, 10 to 14 minutes. Once they are out of the oven, sprinkle evenly with 1/2 tsp salt and serve immediately. Enjoy these with ranch or your favorite dipping sauce.