Preheat your oven to 400℉.
In a mixing bowl whisk together eggs, heavy cream, parmesan cheese, and ½ teaspoon salt.
In an oven-proof skillet heat the olive oil over medium heat. Add the onions, zucchini, mushrooms, remaining 1 teaspoon salt, and pepper. Sauté for 5-8 minutes until soft and the moisture has come out and mostly evaporated.
To the skillet with the sautéd veggies, add the egg mixture and spread everything into an even layer.
Bake for 20-30 minutes until the center is set.
Once you remove it from the oven, let it sit for at least 15 minutes before slicing. Serve with fresh chives and more parmesan cheese if desired.