Preheat the oven to 400F.
In a large bowl, whisk together eggs, cream, and 1/2 teaspoon salt.
In a 12-inch skillet, heat olive oil over medium heat. Add the onion and remaining ½ teaspoon salt. Cook, frequently stirring until onions start to turn translucent, about 5 minutes.
Stir in garlic and cook for 1 minute. Stir in the chopped vegetables. Cook until crisp-tender, about 5 to 8 minutes depending on your vegetables.
Stir in the leafy greens and black pepper. Cook for 1 to 2 minutes, just until wilted.
Spread vegetables evenly over the bottom of the skillet. (Drizzle in another tablespoon of oil if the pan looks dry or the veggies are sticking.) Sprinkle 1 cup cheese over the vegetables. Pour in the egg mixture. Tilt and swirl the pan to evenly distribute the egg mixture if needed. Sprinkle with the remaining 1/2 cup cheese.
Cook until just until the edge starts to set, about 5 minutes. Transfer to the oven.
Bake for 8 minutes or until slightly puffed and the center is set. Sprinkle with extra cheese and garnish with pepper and herbs if desired. Cool for a few minutes before slicing and serving.