Beat eggs gently in a small bowl. Try to avoid making air bubbles.
Pour egg mixture into a non-stick pan (do NOT preheat the pan). Add 1 Tablespoon cold butter.
Turn heat to medium-high. Using a rubber spatula, stir constantly until butter melts and curds begin to form. Remove from heat and continue stirring until soft curds begin to form. You can return the pan to the heat for a few seconds at a time to continue cooking curds if needed. You want soft, creamy eggs. Do not over cook.
Season with salt and pepper after the soft curds have formed. Fold in creme fraiche until eggs are lightly coated. Garnish with green onion (optional) and serve immediately.