Pour the oil into a deep, heavy bottomed pot and heat to 350 degrees F.
Make the breading mixture by combining the breadcrumbs, and Parmesan in a medium bowl. Mix to blend. In another bowl, whisk together the eggs and the splash of water.
Place the zucchini in a large bowl and season with salt. Toss to blend. Sprinkle lightly with flour (use a sieve) to dredge then toss to coat evenly - this will help the breading to stick. Submerge the zucchini in the eggs. Remove the pieces, 1 by 1, shaking off excess egg and them roll them in the breadcrumb mixture until they are coated on all sides. Transfer to a platter or baking sheet.
When the oil comes up to temperature, test the oil by dropping in one piece of zucchini. It should rise to the surface fairly quickly, begin the bubble and fry gradually. Prepare a baking sheet fitted with a kitchen towel and a slotted spoon (or, alternatively, a spider) to remove the zucchini from the oil. Drop a few pieces of zucchini into the oil and gently swirl the oil as they fry. This swirling will allow the zucchini to move around a lot, assuring they fry more evenly on all sides. When they are light to medium brown, remove them with the spoon and lay them out on the kitchen towel to cool. Sprinkle with a touch of salt and paprika. Repeat.