In a medium skillet, heat the oil over medium heat. Add the vegetables and sprinkle with salt and pepper. Sauté until softened, about 5 minutes. Transfer the vegetables to the baking dish and spread them out evenly.
In a large bowl, whisk together the eggs, half and half, salt, and garlic powder.
Pour the egg mixture over the vegetables.
Bake, uncovered, in the preheated oven for 25 minutes. Add the cheese to the top of the casserole and continue baking another 10-15 minutes, until the cheese is melted a knife inserted into the center comes out clean.