Combine eggs, cream and salt in the bowl of a stand mixer fitted with the whisk attachment. Beat eggs until light and creamy.
In a large, non-stick skillet, melt butter over medium heat. When butter just starts to foam, pour beaten eggs in the center of the pan and reduce heat to medium-low.
When eggs are just starting to set, use a spoon or spatula to push the barely set eggs to the top of the pan, allowing the unset egg mixture to run to the center. Continue to do this until most of the egg is set. Then start turning sections of egg over to fully cook the eggs.
Cook the eggs low and slow. Remove the eggs from the heat when fully cooked through, but still slightly shiny. Do not over cook!
If desired, garnish with a little chopped fresh parsley and/or chives.