Beat the eggs with the egg yolk in a bowl until smooth and evenly yellow.
Put the beaten eggs in a small saucepot with the butter. Cook over medium heat, stirring the entire time with a spatula. The eggs should begin to thicken; transferring them on and off the heat will allow you to control the temperature, creating soft creamy eggs. When the eggs start to become thick and soupy, season with salt and pepper. Return to the heat and cook until desired doneness is achieved; if you'd like them cooked more, simply apply more heat.
Mix in the sour cream and garnish with chives if using.