How to Make It
Preheat oven to 400°F. Heat oil in a 9-inch cast-iron or ovenproof skillet over medium-high. Add onion, and cook, stirring occasionally, until softened, about 5 minutes. Add zucchini, and cook, stirring often, until zucchini is tender and brown in spots, 8 to 10 minutes.
Reserve 2 tablespoons cheese and set aside. Whisk together remaining cheese, eggs, salt, pepper, and paprika. Pour over vegetables in skillet, and cook, stirring gently, until eggs just begin to set, about 1 minute. Transfer skillet to preheated oven, and bake until edges are set but center is still slightly loose, 5 to 6 minutes.
Increase oven temperature to broil, and broil until center is set and top is lightly browned, about 2 minutes. Serve topped with reserved Parmesan and parsley.