1. Combine 2 cups flour, next 2 ingredients, and 1 tsp. salt in a shallow dish. Whisk together eggs and 3 Tbsp. water in another dish.
2. Process breadcrumbs in a food processor 10 to 15 seconds or until finely ground. Combine breadcrumbs, 4 Tbsp. flour, oregano, pepper, and remaining 2 tsp. salt in a third shallow dish.
3. Dredge zucchini, in batches, in flour mixture; dip in egg mixture, and dredge in breadcrumb mixture.
4. Pour oil to depth of 2 inches into a Dutch oven; heat over medium heat to 325°. Fry zucchini, in batches, 1 to 2 minutes or until golden. Drain on a wire rack over paper towels. Sprinkle with Parmesan cheese.