Place the bacon slices in a cold skillet and turn the heat to medium, cooking until the fat renders and the strips are deeply browned and crispy.
While the bacon cooks, crack the eggs into a medium bowl and whisk vigorously with the Greek yogurt, sea salt, and black pepper until the mixture is uniform and no white streaks remain.
Remove the bacon from the skillet and drain on a paper towel-lined plate to maintain its crunch.
Wipe out the skillet or use a fresh non-stick pan and melt the ghee over medium-low heat, swirling to coat the bottom completely.
Pour the egg mixture into the pan and let it sit undisturbed for about 30 seconds until the edges begin to set.
Using a silicone spatula, gently push the eggs from the outer edges toward the center, creating large, soft curds.
Continue to cook slowly, stirring occasionally, until the eggs are custardy and just barely set, then remove from heat immediately to prevent overcooking.
Divide the eggs onto plates, garnish with finely chopped fresh chives, and serve alongside the crispy bacon strips.