In a medium bowl, whisk together the large eggs and egg whites until completely combined and slightly frothy.
Heat a high-quality non-stick skillet over medium-low heat and add the ghee, swirling to coat the bottom of the pan.
Pour the egg mixture into the skillet and let it sit for 30 seconds until the edges just begin to set.
Using a silicone spatula, gently push the eggs from the outer edges toward the center, creating large, soft curds.
Continue cooking low and slow, stirring occasionally, until the eggs are mostly set but still look slightly wet and glistening.
Remove the skillet from the heat immediately to prevent overcooking; the residual heat will finish the process.
Slice the avocado into thin wedges and arrange them alongside the fluffy scrambled eggs.
Season the entire plate with sea salt and black pepper, then garnish with finely chopped fresh chives.