Preheat oven to 350 degrees; spray a 9-inch deep-dish pie plate with non-stick cooking spray and set aside.
Separate eggs, placing yolks in a small bowl and scramble slightly; and the whites in a bowl large enough to accomodate a hand mixer and set aside.
In a large skillet over medium-high heat, melt butter and cook onions until translucent; add grated zucchini and carrots.
When zucchini begins to turn watery, add oregano and chicken stock powder; continue to cook until all liquid evaporates. Add salt & pepper if you are using it. Remove from heat and cool slightly.
Add 1 tablespoon of water to the egg whites, and beat with a mixer until stiff peaks form. Fold yolks into egg whites and mix until incorporated (note: egg whites may deflate slightly).
Blend zucchini and carrot mixture in with the eggs, folding gently until all ingredients are incorporated.
Pour mixture into baking dish and sprinkle Parmesan cheese on top.
Bake 30-35 minutes, or until eggs are set. Allow to cool slightly before serving.