Thinly slice zucchini and onion using a mandoline or knife.
In a large bowl, whisk together eggs, 1 teaspoon salt, and ¼ teaspoon pepper. Set aside.
In a large skillet, heat 2 tablespoon olive oil over medium heat.
Add onions and saute, stirring occasionally, for about 5 minutes or until soft and translucent.
Add zucchini to pan. Sprinkle with a bit of salt (¼ tsp) and stir. Continue cooking, stirring occasionally for another 3 or 4 minutes or until zucchini is soft but not falling apart.
Remove from heat and add to seasoned eggs. Stir well.
In an 10 inch, non-stick, frying pan heat 2 teaspoon olive oil over medium-high heat.
Add zucchini and egg mixture to pan and spread everything around evenly.
Lower heat to medium to medium-low. Let cook, without stirring, for approximately 4-5 minutes, adjusting heat if starting to brown too much.
Once egg is starting to set evenly, but not fully cooked, remove from heat. Place a large plate on top of frying pan, it should be bigger than the pan. Over the sink, flip the pan, inverting the omelette onto the plate, cooked side up.
Wipe the pan clean and heat another 2 teaspoon olive oil over medium heat.
Slide the omelette back into the pan, cooked side up. Using a rubber spatula, round the edges by pushing down all around the edges. Reduce heat to medium low.
Continue cooking for another 3-4 minutes, watching that it doesn't brown too much and adjusting heat accordingly. The omelette should feel firm to the touch or you can slice into the middle to check for doneness.
Remove from heat and flip or slide onto a clean plate. Choose the best looking side to be presented. Let rest for at least 15 minutes before serving.
Spanish omelette, or Tortilla de Calabacin, is best served slightly warm or at room temperature and after is has rested.