Preheat the oven to 350 degrees.
Heat the olive oil in a large sauté pan and add the shredded zucchini. Season with the salt and pepper and cook at medium heat, until the zucchini has softened and all of the liquid has been released, about 10-15 minutes. Set aside and let cool.
In a large bowl, beat the eggs and the egg whites together and season with a pinch of salt. Add the cooled zucchini and grated cheeses and stir until well incorporated.
Pour the mixture into a greased baking dish and sprinkle the top with grated Parmesan cheese.
Bake for 40-45 minutes, or until golden brown.