Crack large, fresh eggs into a cold nonstick saucepan. Whisk until smooth and well blended, about 1-2 minutes.

Place the saucepan over the lowest heat. Add unsalted butter, stirring continuously with a spatula until melted.

Continue to stir the mixture, making gentle figure-eights. Cook for about 5 minutes until tiny curds form.

Keep stirring for an additional 4-5 minutes, watching the mixture transform into a custard-like texture.

When the eggs are soft and glossy, remove the pan from heat. Stir in heavy cream or crème fraîche, and season with salt and white pepper.

Spoon the eggs onto warm plates and garnish with chopped chives. Serve immediately.