In a mixing bowl, whisk together the eggs, heavy cream, salt, and pepper until well combined.

Heat the non-stick skillet over medium-low heat and add the butter, allowing it to melt and coat the pan.

Pour the egg mixture into the skillet and let it sit undisturbed for a few seconds until it starts to set around the edges.

Gently stir the eggs with a spatula, pushing them from the edges to the center, and continue to cook until they are softly set but still slightly runny.

Remove the skillet from heat and fold in the shredded cheese until melted and creamy.

Serve immediately, garnished with additional cheese or herbs if desired.