1. Preheat oven to 350°F. Spray a 9-inch square baking dish with nonstick olive oil cooking spray and set aside.
2. In a large skillet, heat oil over medium heat. Add onion and cook, stirring frequently, until softened, about 3 minutes. Add broccoli and cook about 5 minutes or until just tender. Transfer vegetables to prepared pan.
3. In a large bowl, beat together eggs, milk, Romano cheese, salt, pepper and oregano. Whisk in rice flour. Pour egg mixture evenly over vegetables. Sprinkle with paprika and bake until set, about 35 minutes. Cool quiche 10 minutes before serving.