Heat about 1-2 inches of oil in a Dutch oven (I like to use cast iron). You can also use a deep pan.
You want to maintain the heat of the oil around 350 degrees. If it gets much lower, the zucchini will soak up too much oil.
Place flour in a pie plate or shallow bowl.
In a second pie plate or shallow bowl, combine Panko crumbs, Parmesan cheese, and 3/4 teaspoon salt.
Slice zucchini into circles, no thicker than 1/2 inch. Coat in flour, dip in egg mixture, and then coat in Panko crumbs. Fry in batches until golden brown on both sides, about 90 seconds per side. Drain on paper towels and season immediately with salt.