Crack the eggs into a bowl. Add a pinch of salt and a splash of milk if using. Whisk vigorously until the yolks and whites are fully combined and slightly frothy.

Heat a non-stick skillet over medium-low heat. Add the butter and let it melt completely, ensuring it coats the bottom of the pan evenly.

Pour the whisked eggs into the skillet. Let them sit undisturbed for about 10 seconds until the edges start to set slightly.

Using a spatula, gently push the eggs from the edges toward the center, allowing the uncooked eggs to flow to the edges. Repeat this process every few seconds.

Continue cooking and gently stirring until the eggs are mostly set but still slightly runny. Remove from heat immediately—the residual heat will finish cooking them.

Season with freshly ground black pepper and garnish with chopped chives if desired. Serve immediately while hot and creamy.