In a medium-sized mixing bowl, crack the whole eggs and add the liquid egg whites.
Add the plain Greek yogurt, sea salt, and black pepper to the bowl, then whisk vigorously until the mixture is uniform and slightly frothy.
Roughly chop the smoked salmon into bite-sized pieces and finely mince the fresh dill.
Place a non-stick skillet over medium-low heat and add the ghee, allowing it to melt and coat the surface of the pan.
Pour the egg mixture into the skillet and let it sit undisturbed for about 30 seconds until the edges just begin to set.
Using a silicone spatula, gently push the eggs from the outer edges toward the center to create large, soft curds.
When the eggs are mostly cooked but still appear slightly moist, fold in the chopped smoked salmon and half of the fresh dill.
Remove the skillet from the heat immediately to avoid overcooking the salmon; the residual heat will finish setting the eggs.
Transfer to a plate and garnish with the remaining fresh dill before serving.