In a medium bowl, whisk the whole eggs, egg whites, sea salt, and black pepper vigorously until the mixture is very frothy and well-combined.
Place a non-stick skillet over medium-low heat and add the ghee, swirling to coat the bottom of the pan.
Add the baby spinach to the skillet and sauté for 1 minute until just wilted, then remove the spinach and set it aside on a small plate.
Pour the egg mixture into the hot skillet, allowing it to sit undisturbed for about 30 seconds until the edges begin to set.
Using a silicone spatula, gently lift the edges of the omelet and tilt the pan to allow the uncooked egg to flow underneath.
Once the top is mostly set but still slightly moist, sprinkle the sharp cheddar, feta, and sautéed spinach over one half of the eggs.
Carefully fold the empty half of the omelet over the filling and cook for another 60 seconds until the cheese is gooey and melted.
Slide the omelet onto a plate and garnish with the parmesan cheese and sliced green onions before serving.