Place the bacon slices in a cold non-stick skillet and turn the heat to medium.
Cook the bacon until it reaches your desired level of crispiness, flipping occasionally, then transfer to a paper towel-lined plate.
In a small mixing bowl, crack the eggs and add the Greek yogurt, sea salt, and black pepper.
Whisk the egg mixture vigorously until completely smooth and no streaks of yogurt remain.
Wipe out the skillet used for the bacon and place it over medium-low heat, adding the ghee to melt.
Pour the egg mixture into the skillet and let sit for 30 seconds until the edges begin to set.
Using a silicone spatula, gently push the eggs from the edges toward the center, creating soft, creamy folds.
Continue cooking slowly until the eggs are mostly set but still look slightly wet, then remove from heat immediately.
Serve the creamy eggs alongside the crispy bacon and garnish with finely chopped fresh chives.