Preheat the oven to 375 degrees F. Lightly coat a 7- by 11-inch baking dish with cooking spray. Bring a medium saucepan of water to a boil. Add the broccoli and cook until tender-crisp, about 2 minutes. Drain and rinse with cold water to stop the broccoli from cooking further. Transfer the broccoli to the prepared baking dish. In a large bowl, whisk together the eggs, egg whites, water, smoked paprika, salt and pepper. Pour the egg mixture over the broccoli and sprinkle the feta cheese over top. Bake until the casserole is set and a knife inserted in the center comes out clean, about 20 minutes. Cut into 6 pieces. Serve.
