In a mixing bowl, crack the eggs and add salt and pepper. Whisk until well combined and slightly frothy.

Stir in the heavy cream until fully incorporated.

Heat the non-stick skillet over medium-low heat and add the butter, allowing it to melt and foam without browning.

Pour the egg mixture into the skillet and let it sit undisturbed for about 30 seconds.

Using a spatula, gently stir the eggs, pushing them from the edges toward the center. Continue to cook, stirring occasionally, until the eggs are soft and slightly runny.

Remove the skillet from heat when the eggs are still slightly undercooked, as they will continue to cook off the heat.

Garnish with chopped chives and serve immediately on warm plates.