Wash the zucchinis thoroughly and trim off both ends. Slice each zucchini into even 1/2-inch thick rounds and set the slices aside, ready for coating.
In three shallow bowls, set up your breading stations: In the first bowl, mix together the flour, salt, and black pepper. In the second bowl, beat the eggs until smooth. In the third bowl, combine the bread crumbs and grated parmesan cheese. This makes the dipping process quick and organized—I like to arrange the bowls left to right from flour to crumbs for a smooth workflow.
Dredge each zucchini slice (from Step 1) first in the seasoned flour, shaking off any excess. Next, dip it into the beaten eggs, making sure it's fully coated. Finally, press the slice into the bread crumb and parmesan mixture so it's well covered. Place the breaded slices on a plate. Repeat with the remaining zucchini. For extra crispiness, I sometimes press the crumbs onto the slices gently to help them stick better.
Heat the vegetable oil in a large frying pan over medium-high heat until the oil begins to shimmer. Prepare a plate with a paper towel to absorb excess oil. Fry the breaded zucchini slices (from Step 3) in batches, cooking each for 1–2 minutes per side until golden and crispy. Use tongs to transfer fried slices onto the paper towel-lined plate as they finish. Serve the zucchini rounds hot for the best flavor and crunch.