Preheat oven to broil with rack in top third of the oven.

Slice the zucchini and onion crosswise very thinly, preferably on a mandolin. Heat 2 tablespoons olive oil in a large skillet over medium heat, and sauté vegetables for 10 minutes, until tender and just softening but not yet brown. Stir in parsley, season with salt and pepper and set aside to cool for 5 minutes. When slightly cooled, pour vegetables into a large bowl, add the eggs and mix thoroughly. Season again with salt and pepper.

Heat a large, nonstick sauté pan (if using the same one you used to saute the veggies, wipe it out thoroughly) over high heat. When the pan is hot, add the remaining 2 tablespoons olive oil. Swirl the oil around the pan, then pour in the egg mixture, tilting the pan to spread it evenly. Reduce heat to low and cook for 15 minutes, running a spatula around the edges and shaking occasionally, until the center of the frittata is just about set.

Transfer pan to the oven (if your handle is rubber, cover it with aluminum foil before doing so) and broil for 3-4 minutes, until the top of the frittata is evenly browned.

Invert the frittata onto a large serving plate and serve warm or at room temperature.