Preheat oven to 450°F. Line a 9x13 inch baking pan with aluminum foil or grease it well and set aside.Spray two large skillets with cooking spray (or add a bit of oil) and add one pound of broccoli florets to each of them. Cook over medium high heat, stirring occasionally, until the broccoli is tender and starting to brown. (I love using frozen broccoli here, but this will obviously take longer if you started with frozen broccoli instead of fresh.) Add salt and pepper and remove from heat.Add the broccoli to the prepared baking dish. Top with four ounces of shredded cheese. Pour the egg whites on top and then sprinkle the remaining two ounces of cheese on top. Bake in the oven at 450°F for 40-45 minutes, or until the quiche has thoroughly cooked and the top is golden. Slice into twelve pieces and devour.