Preheat the oven with the air circulation on to 200 degrees C. rack set in the middle.
In the meantime, add in a large bowl the eggs and the extra egg whites along with the Yoghurt and season with ½ teaspoon of salt and ½ teaspoon of pepper. Whisk for 2 minutes and then add in the mixture the feta cheese.
In a large, cast iron saucepan over medium heat add the 2 tablespoons of the oil, wait a minute to heat and add the mushrooms and the peppers. Sauté until a bit soft, add the thyme and peperoncino chilies and season with the remaining salt and pepper.
Add the egg mixture along with the parsley, cooking for 3-4 minutes until you notice that the edges start to set. While cooking, with the use of a spatula, lightly get into the edges of the frittata to allow the mixture to move and reach the pan.
Take off the heat and bake in the oven for about 8-10 minutes until puffy. Turn on the broiler and bake for 3 more minutes until nicely browned.