Step 1Heat the broiler. Melt the butter in a 10-inch nonstick skillet over medium heat. Cut the zucchini in lengthwise quarters, then in crosswise pieces, about one-third to one-half-inch thick.
Step 2When the butter sizzles, add the zucchini and cook, stirring occasionally. After 2 to 3 minutes, add the green onions and green chile and cook until the zucchini is tender, about 8 minutes. There should be no liquid in the bottom of the pan. Add the corn and remove from the heat.
Step 3While the zucchini is cooking, beat the eggs with a fork in a mixing bowl just until the yolks and the white are thoroughly mixed, but don't overbeat, which can make the frittata dry. Stir in the salt, the zucchini mixture and half of the cheese and stir to mix well.
Step 4Return the skillet to low heat, cover and cook, without stirring, until the eggs have set, leaving only a top layer uncooked, about 10 minutes. Scatter the remaining cheese over the top and place it under the broiler until the top is browned and puffy, 1 to 2 minutes.
Step 5To unmold the frittata, let it cool slightly in the pan. Use a spatula to loosen it along the sides, and then bang it firmly on a cutting board to release the underside. Slide it out onto a serving plate. Serve either hot or at room temperature. If you're going to refrigerate the frittata, let it return to room temperature before serving.