Preheat oven to 375 degrees. In a 10-inch skillet, warm the olive oil. Sauté the scallions until softened. Add the garlic and cook for 1 minute. Add the zucchini slices and a generous pinch of salt and sauté until tender, about 6 minutes.
In a large mixing bowl, beat the eggs, 1 teaspoon salt, and a few grinds of black pepper. Stir the cooked zucchini mixture and the corn (and grated cheese if using) into the eggs and combine well. Pour the mixture back into the skillet. If using feta or goat cheese, scatter the pieces across the top of the egg mixture.
Transfer skillet to the oven and bake until firm, about 40 minutes.