In a medium bowl, whisk together the eggs, egg whites, sea salt, and black pepper until completely smooth and aerated.
Finely chop the fresh dill and parsley, then fold half of the chopped herbs into the egg mixture.
Place a small skillet over medium-low heat and lightly toast the walnuts for 2-3 minutes until they become fragrant and golden.
Remove the walnuts from the pan and melt the ghee in the same skillet over medium-low heat.
Pour the egg mixture into the skillet and cook slowly, using a spatula to gently push the curds from the edges toward the center.
While the eggs cook, spread the Greek yogurt onto the base of a serving plate and sprinkle with half of the za'atar.
Once the eggs are soft and just set, spoon them over the yogurt base.
Garnish the dish with crumbled feta cheese, toasted walnuts, the remaining za'atar, and the rest of the fresh herbs.