Heat 2 tablespoons oil in a large frying pan or wok.  Add onion to the pan and cook a few minutes.  Then add the mushrooms and garlic and ginger.   Cook, stirring occasionally, until the mushrooms are browned, about 5 minutes.  Stir in the broccoli and the chopped green onions.  Cook briefly, about 1 minute.   Add last tablespoon of oil to the pan and then add the quinoa to the pan and stir.  After everything is mixed together, make a space in the pan and pour in the beaten eggs.  Mix it and incorporate into the rest of the dish.  Stir in the soy sauce, salt, and pepper to taste.  Continue to cook, stirring occasionally, until completely warmed through.   Serve immediately or set aside and reheat when ready.