Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with olive oil.
In a large mixing bowl, combine the cooked quinoa, broccoli, bell peppers, mushrooms, corn, and half of the cheddar cheese.
In a separate bowl, whisk together the milk, eggs, garlic powder, onion powder, salt, pepper, and paprika if using.
Pour the egg mixture over the quinoa and vegetable mixture, stirring until everything is well combined.
Transfer the mixture to the prepared baking dish, spreading it evenly.
Top with the remaining cheddar cheese.
Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for about 5 minutes before serving.