Heat the olive oil in a medium nonstick skillet set over medium heat.
Add the onion and cook, stirring occasionally, until the onions are starting to brown, about 4 minutes.
Add the grated zucchini and cook for 2 minutes. Transfer the vegetables to a plate and cover with foil to keep warm.
In a medium bowl, whisk together the eggs, egg whites and water until combined.
Wipe out the skillet, coat with cooking spray and increase the heat to medium-high.
Add the eggs to the skillet and cook until the edges begin to set. Gently lift the edge of the omelet with a spatula and tilt the pan to allow the uncooked egg mixture to run into the bottom of the pan. Continue to do this as the omelet cooks.
Cook until the center is set. Season with salt and pepper.
Spoon the vegetable mixture onto half of the omelet and top with the feta cheese.
With a spatula, loosen the omelet from the pan and fold it in half. Slide it onto a cutting board. Cut the omelet in half and serve, garnishing with parsley.