Clean and slice the cremini mushrooms into even pieces.
Heat half of the ghee in a non-stick skillet over medium-high heat and sauté the mushrooms until they are golden brown and tender.
Remove the mushrooms from the pan and set them aside on a warm plate.
In a medium bowl, whisk together the whole eggs, egg whites, sea salt, and black pepper until the mixture is frothy and well combined.
Melt the remaining ghee in the same skillet over medium heat, ensuring the bottom is fully coated.
Pour the egg mixture into the pan, letting it set for a moment before gently lifting the edges to allow the raw egg to flow underneath.
When the eggs are mostly set but still slightly moist on top, sprinkle the crumbled feta cheese over one half.
Fold the omelet in half and cook for another minute until the cheese is slightly softened.
Slide the fluffy omelet onto a plate, garnish with fresh chives, and serve with the sautéed mushrooms on the side.