Slice the zucchinis lengthwise and use a spoon to scoop out the seeds. Next, grate the seeded zucchini using a box grater or a food processor. This will provide the base for your patties.
In a medium bowl, combine the grated zucchini (from Step 1), eggs, potato flakes, Parmesan cheese, mozzarella cheese, diced onion, and a pinch of salt. Stir the mixture until everything is well-combined and evenly mixed. I like to squeeze the grated zucchini gently to remove some excess moisture before mixing, which helps the patties hold together better.
Heat the vegetable oil in a large skillet over medium heat. While the oil heats up, form the zucchini mixture (from Step 2) into 8 round patties, each about 3/4-inch thick. Place the patties in the hot oil and cook for 2-3 minutes on each side, or until they become golden brown and crispy.
Transfer the cooked patties onto a plate lined with paper towels to drain any excess oil. Let them cool slightly before serving. For extra deliciousness, I sometimes sprinkle a little extra Parmesan on top right after frying.