Pour enough oil into a large frying pan to reach a depth of 2 inches. Heat the oil over medium heat until a deep-fry thermometer registers 350 degrees F.
Stir 1 1/2 cups Parmesan, the panko, and salt in a medium bowl to blend. Whisk the eggs in another medium bowl to blend. Working in batches, dip the zucchini in the eggs to coat completely and allow the excess egg to drip back into the bowl. Coat the zucchini in the panko mixture, patting to adhere and coat completely. Place the zucchini strips on a baking sheet.
When the oil is hot, working in batches, fry the zucchini sticks until they are golden brown, about 3 minutes. Using a slotted spoon, transfer the fried zucchini to paper towels and drain.
Arrange the fried zucchini on a platter. Sprinkle with the remaining Parmesan and serve.