Preheat oven to 400ºF.
In a medium bowl whisk together eggs, parsley, Parmigiano-Reggiano, cream and some salt and pepper. Set aside.
Trim zucchini ends and grate each one lengthwise over a box grater to take the flesh off without pulling out any of the seeds. Place a medium skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Sauté the leeks and zucchini until tender, about 5 minutes. Season with salt and pepper.