
Preheat the oven to 375°F. Grease a 9-inch pie dish with butter or cooking spray.
In a medium skillet over medium heat, melt the butter. Add the mushrooms and sauté until softened and browned, about 5 minutes. Add the zucchini and onion on top of the mushrooms, and cook until softened and lightly browned, about 10 more minutes. Add to the pie dish and sprinkle with ½ cup cheddar cheese.
In a large bowl, whisk together the eggs, milk, salt, pepper, and oregano until well combined. Pour the mixture over the vegetables and cheese, and sprinkle with the remaining ½ cup cheese.
Bake for 30–35 minutes, until the center sets and a knife inserted in the middle comes out clean.
Let cool for about 10 minutes before cutting and serving.