Place the bacon slices in a cold skillet and turn the heat to medium, cooking until the fat has rendered and the bacon is golden and crispy.
While the bacon cooks, whisk the whole eggs, egg whites, Greek yogurt, sea salt, and black pepper in a bowl until the mixture is completely smooth and no streaks of yogurt remain.
Remove the crispy bacon from the pan and set it aside on a paper towel-lined plate, leaving only a very thin coating of bacon fat in the skillet.
Lower the heat to medium-low and add the ghee to the skillet, swirling to coat the bottom.
Pour the egg mixture into the skillet and let it sit for 20 seconds until the edges begin to set.
Using a silicone spatula, gently push the eggs from the edges toward the center, stirring constantly to create soft, small curds.
Remove the skillet from the heat when the eggs still look slightly wet, as they will continue to firm up from the residual heat.
Transfer the creamy eggs to a plate, garnish with finely chopped fresh chives, and serve immediately with the crispy bacon strips.