In a medium bowl, whisk together the eggs, heavy cream, salt, and black pepper until well combined and slightly frothy.
Heat a non-stick skillet over low heat and add the butter. Allow it to melt and coat the bottom of the skillet.
Pour the egg mixture into the skillet. Let it sit undisturbed for about 30 seconds until the edges start to set.
Gently stir the eggs with a spatula, pushing them from the edges toward the center. Continue to cook, stirring occasionally, until the eggs are softly set and slightly runny in places, about 3-5 minutes.
Remove the skillet from heat. The residual heat will continue to cook the eggs, so be careful not to overcook them.
Serve immediately, garnished with chopped chives or parsley if desired.