In a mixing bowl, crack the eggs and beat them gently with a whisk until well blended. Gradually add the heavy cream, and season with salt and pepper. Set aside.

Melt unsalted butter in a non-stick skillet over low heat, ensuring it becomes frothy without browning. Swirl the butter to coat the pan.

Pour the egg mixture into the skillet, ensuring it spreads evenly. Stir gently in a circular motion for 5-7 minutes until just set but still soft.

Chop the chives and sprinkle them over the eggs, gently folding them in. Cook for another minute until incorporated.

Remove from heat, transfer to warm plates, and garnish with additional chives. Serve immediately.