In a bowl, whisk together the eggs, salt, and pepper until well combined.
Heat a non-stick skillet over medium-low heat. Add the butter to the pan and swirl it around until it's completely melted. Once the butter is melted, add in the eggs and immediately start to stir with a rubber spatula.
Use the spatula to constantly push and pull the eggs around the pan. It may take a few minutes for the eggs to start to solidify. Once the eggs are about halfway set (so still a bit wet) mix in the cheese.
Cook until the eggs are mostly set but still a little glossy/wet. Remove from the heat (the eggs will continue to cook even after being removed from the heat).
Serve while still warm, and top with freshly chopped chives and flaky sea salt.