In frying pan, heat 1 tablespoon of oil, add sliced onions and saute until wilted.  Add zucchini and cook until tender - about 10 mins.  Add basil and remove from heat.  Pour into strainer and let drain.

In a bowl, beat eggs, add cheese and mix well.  Add drained zucchini mixture.

Heat 1 tablespoon oil in frying pan.  Add egg mixture.  Distribute the mixture evenly in the pan.  Lower the heat and cook until set - 12 - 14 mins.

Place a large dish on top of the frying pan and invert the frittata.  Carefully slide the upside down frittata back into the frying pan and let cook 2 mins longer.  Invert onto a dish and serve.  Cut the frittata into wedges, the same way you would cut a pie.