In a medium bowl, mix the eggs, sour cream, mustard, salt, and black pepper.
Heat the butter in a 10-inch skillet until melted. Add the onions and cook over medium-low heat until softened.
Pour the egg mixture into the skillet. As the eggs cook, lift the moisture from the bottom and sides of the pan so the uncooked part flows to the bottom. Cook until the eggs are thick and creamy, throughout, but still moist.