Preheat the oven to 350°F. Grease a 9x13-inch baking dish with cooking spray or olive oil.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and minced garlic, sautéing until the onion is translucent, about 3-4 minutes.
Add the sliced zucchini and corn to the skillet. Cook for an additional 5-7 minutes until the zucchini is tender. Remove from heat and let cool slightly.
In a large bowl, whisk together the milk, eggs, oregano, salt, and black pepper. Stir in the sautéed vegetable mixture.
Fold in the shredded cheddar cheese and breadcrumbs until well combined. Pour the mixture into the prepared baking dish and spread evenly.
Sprinkle the grated Parmesan cheese on top. Bake in the preheated oven for 30-35 minutes, or until the casserole is set and the top is golden brown.
Let the casserole cool for 5-10 minutes before serving to allow it to firm up for easier slicing.