Divide eggs, flour, and parmesan cheese between three medium-sized bowls. Whisk both eggs.
Slice zucchini into round, uniformly thin slices either with a sharp knife or mandolin. Toss zucchini slices in egg, then a thin layer of flour. Then, toss in egg again, followed by parmesan cheese.
Place vegetable oil into a large pan. Fire up pan to high heat and wait until the oil is sizzling hot. Sauté zucchini rounds 2 minutes per side. Lightly sprinkle salt and pepper on each side. Once finished, set on a paper towel to absorb oil and let cool for five minutes.