1. Crack 3 eggs into a small bowl and whisk with a fork until the whites and eggs are just combined, about 10 seconds. Transfer beaten eggs to skillet.
2. Let eggs sit until they just begin to stick to the bottom of the skillet, about 30 seconds. Begin stirring vigorously with a wooden spoon to break up the curds. Cook, stirring constantly, until eggs are almost set but still runny, 3-4 minutes.
3. Add salt, butter, heavy cream, and fresh chives and stir to combine. Return the skillet to medium-low heat and cook, stirring occasionally, until the eggs cook to desired doneness, 1-2 minutes.
4. Transfer to a plate and season with freshly ground black pepper to taste and finely chopped chives.
