Heat vegetable oil in a large skillet over medium high heat.
In a large bowl, combine Panko and Parmesan; set aside.
Working in batches, dredge zucchini rounds in flour, dip into eggs, then dredge in Panko mixture, pressing to coat.
Add zucchini rounds to the skillet, 5 or 6 at a time, and cook until evenly golden and crispy, about 1 minute on each side.
Transfer to a paper towel-lined plate. Serve immediately.